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Journal articles on the topic 'Pathwise approach'

Author: Grafiati

Published: 10 March 2023

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1

Kühn, C., A. E. Kyprianou, and K. van Schaik. "Pricing Israeli options: a pathwise approach." Stochastics 79, no. 1-2 (2007): 117–37. http://dx.doi.org/10.1080/17442500600976442.

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2

Willinger, Walter. "A pathwise approach to stochastic integration." Stochastic Processes and their Applications 26 (1987): 236. http://dx.doi.org/10.1016/0304-4149(87)90177-3.

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3

Cattiaux, Patrick. "A Pathwise Approach of Some Classical Inequalities." Potential Analysis 20, no. 4 (2004): 361–94. http://dx.doi.org/10.1023/b:pota.0000009847.84908.6f.

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4

Abdullin, Marat Airatovich, Niyaz Salavatovich Ismagilov, and Farit Sagitovich Nasyrov. "One dimensional stochastic differential equations: pathwise approach." Ufimskii Matematicheskii Zhurnal 5, no. 4 (2013): 3–15. http://dx.doi.org/10.13108/2013-5-4-3.

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5

Korytowski, Adam, and Maciej Szymkat. "Necessary Optimality Conditions for a Class of Control Problems with State Constraint." Games 12, no. 1 (2021): 9. http://dx.doi.org/10.3390/g12010009.

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An elementary approach to a class of optimal control problems with pathwise state constraint is proposed. Based on spike variations of control, it yields simple proofs and constructive necessary conditions, including some new characterizations of optimal control. Two examples are discussed.

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6

Jin, Xing, Dan Luo, and Xudong Zeng. "Dynamic Asset Allocation with Uncertain Jump Risks: A Pathwise Optimization Approach." Mathematics of Operations Research 43, no. 2 (2018): 347–76. http://dx.doi.org/10.1287/moor.2017.0854.

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7

BOUHADOU, S., and Y. OUKNINE. "STOCHASTIC EQUATIONS OF PROCESSES WITH JUMPS." Stochastics and Dynamics 14, no. 01 (2013): 1350006. http://dx.doi.org/10.1142/s0219493713500068.

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We consider one-dimensional stochastic differential equations driven by white noises and Poisson random measure. We introduce new techniques based on local time prove new results on pathwise uniqueness and comparison theorems. Our approach is very easy to handle and do not need any approximation approach. Similar equations without jumps were studied in the same context by [8, 12] and other authors.

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8

Catuogno, Pedro, and Christian Olivera. "Renormalized-generalized solutions for the KPZ equation." Infinite Dimensional Analysis, Quantum Probability and Related Topics 17, no. 04 (2014): 1450027. http://dx.doi.org/10.1142/s0219025714500271.

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This work introduces a new notion of solution for the KPZ equation, in particular, our approach encompasses the Cole–Hopf solution. We set in the context of the distribution theory the proposed results by Bertini and Giacomin from the mid '90s. This new approach provides a pathwise notion of solution as well as a structured approximation theory. The developments are based on regularization arguments from the theory of distributions.

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9

Bianchi, A., A. Gaudillière, and P. Milanesi. "On Soft Capacities, Quasi-stationary Distributions and the Pathwise Approach to Metastability." Journal of Statistical Physics 181, no. 3 (2020): 1052–86. http://dx.doi.org/10.1007/s10955-020-02618-9.

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10

Westphal, U., and T. Schwartz. "Farthest points and monotone operators." Bulletin of the Australian Mathematical Society 58, no. 1 (1998): 75–92. http://dx.doi.org/10.1017/s0004972700032019.

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We apply the theory of monotone operators to study farthest points in closed bounded subsets of real Banach spaces. This new approach reveals the intimate connection between the farthest point mapping and the subdifferential of the farthest distance function. Moreover, we prove that a typical exception set in the Baire category sense is pathwise connected. Stronger results are obtained in Hilbert spaces.

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11

LIM, ENG LIAN, JOHN McCALLUM, and KWOK HUNG CHAN. "PRODUCTION-GRAPH: A GRAPH THEORETICAL MODEL FOR CHECKING KNOWLEDGE BASE ANOMALIES." International Journal on Artificial Intelligence Tools 01, no. 04 (1992): 563–95. http://dx.doi.org/10.1142/s0218213092000065.

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Knowledge acquisition is tedious and error-prone. Consequently, a knowledge base may be inconsistent, and contains unreachable rules, redundant rules, and rules which may lead to deadends and infinite loops. There are three approaches for checking these anomalies: interactive, non-interactive pairwise and non-interactive pathwise. In this article, we will present a graph theoretical model called Production-graph for checking knowledge base anomalies along the non-interactive pathwise approach. Production-graph uses graph theoretical constructions to represent facts and rules, as well as releva

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12

Deng, Mengting, Guo Jiang, and Ting Ke. "Numerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions." Discrete Dynamics in Nature and Society 2021 (October 30, 2021): 1–11. http://dx.doi.org/10.1155/2021/4934658.

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This paper presents a valid numerical method to solve nonlinear stochastic Itô–Volterra integral equations (SIVIEs) driven by fractional Brownian motion (FBM) with Hurst parameter H ∈ 1 / 2 , 1 . On the basis of FBM and block pulse functions (BPFs), a new stochastic operational matrix is proposed. The nonlinear stochastic integral equation is converted into a nonlinear algebraic equation by this method. Furthermore, error analysis is given by the pathwise approach. Finally, two numerical examples exhibit the validity and accuracy of the approach.

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13

Braunsteins, Peter, Geoffrey Decrouez, and Sophie Hautphenne. "A pathwise approach to the extinction of branching processes with countably many types." Stochastic Processes and their Applications 129, no. 3 (2019): 713–39. http://dx.doi.org/10.1016/j.spa.2018.03.013.

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14

Alnafisah, Yousef. "A New Approach to Compare the Strong Convergence of the Milstein Scheme with the Approximate Coupling Method." Fractal and Fractional 6, no. 6 (2022): 339. http://dx.doi.org/10.3390/fractalfract6060339.

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Milstein and approximate coupling approaches are compared for the pathwise numerical solutions to stochastic differential equations (SDE) driven by Brownian motion. These methods attain an order one convergence under the nondegeneracy assumption of the diffusion term for the approximate coupling method. We use MATLAB to simulate these methods by applying them to a particular two-dimensional SDE. Then, we analyze the performance of both methods and the amount of time required to obtain the result. This comparison is essential in several areas, such as stochastic analysis, financial mathematics,

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15

Wang, Peiguang, and Yan Xu. "Averaging Method for Neutral Stochastic Delay Differential Equations Driven by Fractional Brownian Motion." Journal of Function Spaces 2020 (May 29, 2020): 1–7. http://dx.doi.org/10.1155/2020/5212690.

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In this paper, we investigate the stochastic averaging method for neutral stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H∈1/2,1. By using the linear operator theory and the pathwise approach, we show that the solutions of neutral stochastic delay differential equations converge to the solutions of the corresponding averaged stochastic delay differential equations. At last, an example is provided to illustrate the applications of the proposed results.

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16

Posilicano, Andrea, and Stefania Ugolini. "Scattering into cones and flux across surfaces in quantum mechanics: A pathwise probabilistic approach." Journal of Mathematical Physics 43, no. 11 (2002): 5386–99. http://dx.doi.org/10.1063/1.1504884.

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17

León, Jorge A., Josep L. Solé, and Josep Vives. "A pathwise approach to backward and forward stochastic differential equations on the poisson space*." Stochastic Analysis and Applications 19, no. 5 (2001): 0. http://dx.doi.org/10.1081/sap-120000223.

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18

Caruana, Michael, Peter K. Friz, and Harald Oberhauser. "A (rough) pathwise approach to a class of non-linear stochastic partial differential equations." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 28, no. 1 (2011): 27–46. http://dx.doi.org/10.1016/j.anihpc.2010.11.002.

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19

Bocar, Ba Demba, Diop Bou, and Thioune Moussa. "AN APPROACH TO PATHWISE STOCHASTIC INTEGRATION IN FRACTIONAL BESOV-TYPE SPACES BY KRYLOV INEQUALITY." Universal Journal of Mathematics and Mathematical Sciences 18 (January 6, 2023): 67–83. http://dx.doi.org/10.17654/2277141723005.

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20

Sheppard, Patrick W., Muruhan Rathinam, and Mustafa Khammash. "A pathwise derivative approach to the computation of parameter sensitivities in discrete stochastic chemical systems." Journal of Chemical Physics 136, no. 3 (2012): 034115. http://dx.doi.org/10.1063/1.3677230.

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21

Landriault, David, Bin Li, and Hongzhong Zhang. "A unified approach for drawdown (drawup) of time-homogeneous Markov processes." Journal of Applied Probability 54, no. 2 (2017): 603–26. http://dx.doi.org/10.1017/jpr.2017.20.

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AbstractDrawdown (respectively, drawup) of a stochastic process, also referred as the reflected process at its supremum (respectively, infimum), has wide applications in many areas including financial risk management, actuarial mathematics, and statistics. In this paper, for general time-homogeneous Markov processes, we study the joint law of the first passage time of the drawdown (respectively, drawup) process, its overshoot, and the maximum of the underlying process at this first passage time. By using short-time pathwise analysis, under some mild regularity conditions, the joint law of the

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22

Crisan, D., P. Dobson, and M. Ottobre. "Uniform in time estimates for the weak error of the Euler method for SDEs and a pathwise approach to derivative estimates for diffusion semigroups." Transactions of the American Mathematical Society 374, no. 5 (2021): 3289–330. http://dx.doi.org/10.1090/tran/8301.

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We present a criterion for uniform in time convergence of the weak error of the Euler scheme for Stochastic Differential equations (SDEs). The criterion requires (i) exponential decay in time of the space-derivatives of the semigroup associated with the SDE and (ii) bounds on (some) moments of the Euler approximation. We show by means of examples (and counterexamples) how both (i) and (ii) are needed to obtain the desired result. If the weak error converges to zero uniformly in time, then convergence of ergodic averages follows as well. We also show that Lyapunov-type conditions are neither su

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23

BERGLUND, NILS, and BARBARA GENTZ. "METASTABILITY IN SIMPLE CLIMATE MODELS: PATHWISE ANALYSIS OF SLOWLY DRIVEN LANGEVIN EQUATIONS." Stochastics and Dynamics 02, no. 03 (2002): 327–56. http://dx.doi.org/10.1142/s0219493702000455.

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We consider simple stochastic climate models, described by slowly time-dependent Langevin equations. We show that when the noise intensity is not too large, these systems can spend substantial amounts of time in metastable equilibrium, instead of adiabatically following the stationary distribution of the frozen system. This behavior can be characterized by describing the location of typical paths, and bounding the probability of atypical paths. We illustrate this approach by giving a quantitative description of phenomena associated with bistability, for three famous examples of simple climate

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24

Ceci, Claudia, and Katia Colaneri. "Nonlinear Filtering for Jump Diffusion Observations." Advances in Applied Probability 44, no. 03 (2012): 678–701. http://dx.doi.org/10.1017/s0001867800005838.

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We deal with the filtering problem of a general jump diffusion process,X, when the observation process,Y, is a correlated jump diffusion process having common jump times withX. In this setting, at any timetthe σ-algebraprovides all the available information aboutXt, and the central goal is to characterize the filter, πt, which is the conditional distribution ofXtgiven observations. To this end, we prove that πtsolves the Kushner-Stratonovich equation and, by applying the filtered martingale problem approach (see Kurtz and Ocone (1988)), that it is the unique weak solution to this equation. Und

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25

Ceci, Claudia, and Katia Colaneri. "Nonlinear Filtering for Jump Diffusion Observations." Advances in Applied Probability 44, no. 3 (2012): 678–701. http://dx.doi.org/10.1239/aap/1346955260.

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We deal with the filtering problem of a general jump diffusion process, X, when the observation process, Y, is a correlated jump diffusion process having common jump times with X. In this setting, at any time t the σ-algebra provides all the available information about Xt, and the central goal is to characterize the filter, πt, which is the conditional distribution of Xt given observations . To this end, we prove that πt solves the Kushner-Stratonovich equation and, by applying the filtered martingale problem approach (see Kurtz and Ocone (1988)), that it is the unique weak solution to this eq

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26

BEVERIDGE, CHRISTOPHER, and MARK JOSHI. "THE EFFICIENT COMPUTATION OF PRICES AND GREEKS FOR CALLABLE RANGE ACCRUALS USING THE DISPLACED-DIFFUSION LMM." International Journal of Theoretical and Applied Finance 17, no. 01 (2014): 1450001. http://dx.doi.org/10.1142/s0219024914500010.

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We study the simulation of range accrual coupons when valuing callable range accruals in the displaced-diffusion LIBOR market model (DDLMM). We introduce a number of new improvements that lead to significant efficiency improvements, and explain how to apply the adjoint-improved pathwise method to calculate deltas and vegas under the new improvements, which was not previously possible for callable range accruals. One new improvement is based on using a Brownian-bridge-type approach for simulating the range accrual coupons. We consider a variety of examples, including when the reference rate is

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27

Boumezoued, Alexandre. "Population viewpoint on Hawkes processes." Advances in Applied Probability 48, no. 2 (2016): 463–80. http://dx.doi.org/10.1017/apr.2016.10.

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AbstractIn this paper we focus on a class of linear Hawkes processes with general immigrants. These are counting processes with shot-noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of the age pyramid which evolves according to immigration and births. The virtue of this approach that combines an intensity process definition and a branching representation is that the population age pyramid keeps track of all past events. This is used to compute new distribution properties for a class of Hawkes processes with general immigrants

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28

Angiuli, Andrea, Christy V. Graves, Houzhi Li, Jean-François Chassagneux, François Delarue, and René Carmona. "Cemracs 2017: numerical probabilistic approach to MFG." ESAIM: Proceedings and Surveys 65 (2019): 84–113. http://dx.doi.org/10.1051/proc/201965084.

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This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [29], and by Huang, Caines, and Malhamé, see [26]. Generally speaki

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29

Nika, Zsolt, and Tamás Szabados. "Strong approximation of Black-Scholes theory based on simple random walks." Studia Scientiarum Mathematicarum Hungarica 53, no. 1 (2016): 93–129. http://dx.doi.org/10.1556/012.2016.53.1.1331.

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A basic model in financial mathematics was introduced by Black, Scholes and Merton in 1973. A classical discrete approximation in distribution is the binomial model given by Cox, Ross and Rubinstein in 1979. In this work we give a strong (almost sure, pathwise) discrete approximation of the BSM model using a suitable nested sequence of simple, symmetric random walks. The approximation extends to the stock price process, the value process, the replicating portfolio, and the greeks. An important tool in the approximation is a discrete version of the Feynman-Kac formula as well. Our aim is to sho

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30

Vaddireddy, Harsha, and Omer San. "Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach." Fluids 4, no. 2 (2019): 111. http://dx.doi.org/10.3390/fluids4020111.

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Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set o

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31

Milstein, Grigori N., and John Schoenmakers. "Uniform approximation of the Cox-Ingersoll-Ross process." Advances in Applied Probability 47, no. 4 (2015): 1132–56. http://dx.doi.org/10.1239/aap/1449859803.

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The Doss-Sussmann (DS) approach is used for uniform simulation of the Cox-Ingersoll-Ross (CIR) process. The DS formalism allows us to express trajectories of the CIR process through solutions of some ordinary differential equation (ODE) depending on realizations of a Wiener process involved. By simulating the first-passage times of the increments of the Wiener process to the boundary of an interval and solving the ODE, we uniformly approximate the trajectories of the CIR process. In this respect special attention is payed to simulation of trajectories near 0. From a conceptual point of view th

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32

Milstein, Grigori N., and John Schoenmakers. "Uniform approximation of the Cox-Ingersoll-Ross process." Advances in Applied Probability 47, no. 04 (2015): 1132–56. http://dx.doi.org/10.1017/s0001867800049041.

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The Doss-Sussmann (DS) approach is used for uniform simulation of the Cox-Ingersoll-Ross (CIR) process. The DS formalism allows us to express trajectories of the CIR process through solutions of some ordinary differential equation (ODE) depending on realizations of a Wiener process involved. By simulating the first-passage times of the increments of the Wiener process to the boundary of an interval and solving the ODE, we uniformly approximate the trajectories of the CIR process. In this respect special attention is payed to simulation of trajectories near 0. From a conceptual point of view th

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33

Catuogno, Pedro José, Sebastián Esteban Ferrando, and Alfredo Lázaro González. "Efficient Hedging of Options with Probabilistic Haar Wavelets." ISRN Probability and Statistics 2012 (September 18, 2012): 1–37. http://dx.doi.org/10.5402/2012/946415.

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The paper brings forward the issue of efficient representations of financial claims; in particular it addresses the problem of large transaction costs in hedging replications. Inspired by the localized properties of wavelets basis, Haar systems associated with space-time discretizations of continuous stochastic processes are proposed as a means to address the issue of efficient pathwise approximation. Theoretical developments are presented that justify the use of these approximations to construct self-financing portfolios by means of binary options. Upper bounds on the volume of transactions r

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Perry, D., W. Stadje, and S. Zacks. "A Duality Approach to Queues with Service Restrictions and Storage Systems with State-Dependent Rates." Journal of Applied Probability 50, no. 3 (2013): 612–31. http://dx.doi.org/10.1239/jap/1378401226.

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Based on pathwise duality constructions, several new results on truncated queues and storage systems of the G/M/1 type are derived by transforming the workload (content) processes into certain ‘dual’ M/G/1-type processes. We consider queueing systems in which (a) any service requirement that would increase the total workload beyond the capacity is truncated so as to keep the associated sojourn time below a certain constant, or (b) new arrivals do not enter the system if they have to wait more than one time unit in line. For these systems, we derive the steady-state distributions of the workloa

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Perry, D., W. Stadje, and S. Zacks. "A Duality Approach to Queues with Service Restrictions and Storage Systems with State-Dependent Rates." Journal of Applied Probability 50, no. 03 (2013): 612–31. http://dx.doi.org/10.1017/s0021900200009748.

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Based on pathwise duality constructions, several new results on truncated queues and storage systems of the G/M/1 type are derived by transforming the workload (content) processes into certain ‘dual’ M/G/1-type processes. We consider queueing systems in which (a) any service requirement that would increase the total workload beyond the capacity is truncated so as to keep the associated sojourn time below a certain constant, or (b) new arrivals do not enter the system if they have to wait more than one time unit in line. For these systems, we derive the steady-state distributions of the workloa

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El-Taha, Muhammad, and Shaler Stidham. "Sample-path stability conditions for multiserver input-output processes." Journal of Applied Mathematics and Stochastic Analysis 7, no. 3 (1994): 437–56. http://dx.doi.org/10.1155/s1048953394000353.

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We extend our studies of sample-path stability to multiserver input-output processes with conditional output rates that may depend on the state of the system and other auxiliary processes. Our results include processes with countable as well as uncountable state spaces. We establish rate stability conditions for busy period durations as well as the input during busy periods. In addition, stability conditions for multiserver queues with possibly heterogeneous servers are given for the workload, attained service, and queue length processes. The stability conditions can be checked from parameters

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37

ROUSSET, MATHIAS, and GIOVANNI SAMAEY. "INDIVIDUAL-BASED MODELS FOR BACTERIAL CHEMOTAXIS IN THE DIFFUSION ASYMPTOTICS." Mathematical Models and Methods in Applied Sciences 23, no. 11 (2013): 2005–37. http://dx.doi.org/10.1142/s0218202513500243.

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We discuss velocity-jump models for chemotaxis of bacteria with an internal state that allows the velocity-jump rate to depend on the memory of the chemoattractant concentration along their path of motion. Using probabilistic techniques, we provide a pathwise result that shows that the considered process converges to an advection-diffusion process in the (long-time) diffusion limit. We also (re-)prove using the same approach that the same limiting equation arises for a related, simpler process with direct sensing of the chemoattractant gradient. Additionally, we propose a time discretization t

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JOSHI, MARK, and OH KANG KWON. "LEAST SQUARES MONTE CARLO CREDIT VALUE ADJUSTMENT WITH SMALL AND UNIDIRECTIONAL BIAS." International Journal of Theoretical and Applied Finance 19, no. 08 (2016): 1650048. http://dx.doi.org/10.1142/s0219024916500485.

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Credit value adjustment (CVA) and related charges have emerged as important risk factors following the Global Financial Crisis. These charges depend on uncertain future values of underlying products, and are usually computed by Monte Carlo simulation. For products that cannot be valued analytically at each simulation step, the standard market practice is to use the regression functions from least squares Monte Carlo method to approximate their values. However, these functions do not necessarily provide accurate approximations to product values over all simulated paths and can result in biases

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Cathcart, Mark J., Hsiao Yen Lok, Alexander J. McNeil, and Steven Morrison. "CALCULATING VARIABLE ANNUITY LIABILITY “GREEKS” USING MONTE CARLO SIMULATION." ASTIN Bulletin 45, no. 2 (2015): 239–66. http://dx.doi.org/10.1017/asb.2014.31.

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AbstractThe implementation of hedging strategies for variable annuity products requires the calculation of market risk sensitivities (or “Greeks”). The complex, path-dependent nature of these products means that these sensitivities are typically estimated by Monte Carlo methods. Standard market practice is to use a “bump and revalue” method in which sensitivities are approximated by finite differences. As well as requiring multiple valuations of the product, this approach is often unreliable for higher-order Greeks, such as gamma, and alternative pathwise (PW) and likelihood-ratio estimators s

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Komyakov, B. K., B. G. Guliev, A. V. Zagazezhev, and R. V. Aliev. "SURGICAL TREATMENT OF PATIENTS WITH OBSTRUCTION OF PYELOURETERAL SEGMENT." Grekov's Bulletin of Surgery 174, no. 3 (2015): 24–28. http://dx.doi.org/10.24884/0042-4625-2015-174-3-24-28.

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The article presents the operation results of 380 patients (170 (44,7%) men and 210 (55,3%) women) with obstruction of pyeloureteral segment at the period from 1996 to 2014. The middle age was 43,2±7,6 years old. Primary strictures took place in 302 (79,5%) patients and recurrent strictures - in 78 (20,5%). Open and laparoscopic plastic operations were performed in 248 (65,2%), endoscopic surgery - in 112 (29,5%), organo-removal surgery - in 20 (5,3%) cases out of 380 patients with obstruction of pyeloureteral segment. The hines Andersen open pyeloplasty was carried out in 142 (37,4%) patients

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Fekete, D., J. Fontbona, and A. E. Kyprianou. "Skeletal stochastic differential equations for continuous-state branching processes." Journal of Applied Probability 56, no. 4 (2019): 1122–50. http://dx.doi.org/10.1017/jpr.2019.67.

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AbstractIt is well understood that a supercritical continuous-state branching process (CSBP) is equal in law to a discrete continuous-time Galton–Watson process (the skeleton of prolific individuals) whose edges are dressed in a Poissonian way with immigration which initiates subcritical CSBPs (non-prolific mass). Equally well understood in the setting of CSBPs and superprocesses is the notion of a spine or immortal particle dressed in a Poissonian way with immigration which initiates copies of the original CSBP, which emerges when conditioning the process to survive eternally. In this article

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42

van der Laan, Mark J., and Alexander R. Luedtke. "Targeted Learning of the Mean Outcome under an Optimal Dynamic Treatment Rule." Journal of Causal Inference 3, no. 1 (2015): 61–95. http://dx.doi.org/10.1515/jci-2013-0022.

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AbstractWe consider estimation of and inference for the mean outcome under the optimal dynamic two time-point treatment rule defined as the rule that maximizes the mean outcome under the dynamic treatment, where the candidate rules are restricted to depend only on a user-supplied subset of the baseline and intermediate covariates. This estimation problem is addressed in a statistical model for the data distribution that is nonparametric beyond possible knowledge about the treatment and censoring mechanism. This contrasts from the current literature that relies on parametric assumptions. We est

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Pu, Shusen, and Peter J. Thomas. "Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics." Neural Computation 32, no. 10 (2020): 1775–835. http://dx.doi.org/10.1162/neco_a_01312.

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Fox and Lu introduced a Langevin framework for discrete-time stochastic models of randomly gated ion channels such as the Hodgkin-Huxley (HH) system. They derived a Fokker-Planck equation with state-dependent diffusion tensor [Formula: see text] and suggested a Langevin formulation with noise coefficient matrix [Formula: see text] such that SS[Formula: see text]. Subsequently, several authors introduced a variety of Langevin equations for the HH system. In this article, we present a natural 14-dimensional dynamics for the HH system in which each directed edge in the ion channel state transitio

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Kong, Benjamin Y., Hao-Wen Sim, Anna K. Nowak, et al. "LUMOS - Low and Intermediate Grade Glioma Umbrella Study of Molecular Guided TherapieS at relapse: Protocol for a pilot study." BMJ Open 11, no. 12 (2021): e054075. http://dx.doi.org/10.1136/bmjopen-2021-054075.

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IntroductionGrades 2 and 3 gliomas (G2/3 gliomas), when combined, are the second largest group of malignant brain tumours in adults. The outcomes for G2/3 gliomas at progression approach the dismal outcomes for glioblastoma (GBM), yet there is a paucity of trials for Australian patients with relapsed G2/3 gliomas compared with patients with GBM. LUMOS will be a pilot umbrella study for patients with relapsed G2/3 gliomas that aims to match patients to targeted therapies based on molecular screening with contemporaneous tumour tissue. Participants in whom no actionable or no druggable mutation

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Duc, Luu Hoang. "Exponential stability of stochastic systems: A pathwise approach." Stochastics and Dynamics, April 18, 2022. http://dx.doi.org/10.1142/s0219493722400123.

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We provide a pathwise approach using semigroup technique to study the asymptotic stability for stochastic differential equations which admit a unique equilibrium. The driving noises in consideration are [Formula: see text] — Hölder continuous with [Formula: see text], so that the perturbed systems can be solved using rough path theory, where the rough integrals are interpreted in the Gubinelli sense for controlled rough paths. Our approach suggests an alternative method for stochastic systems with standard Brownian noises, by not using Itô formula but a relaxed isometry property of Itô stochas

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Gubinelli, Massimiliano, Peter Imkeller, and Nicolas Perkowski. "A Fourier analytic approach to pathwise stochastic integration." Electronic Journal of Probability 21 (2016). http://dx.doi.org/10.1214/16-ejp3868.

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Fernandez, Roberto, Francesco Manzo, Francesca Nardi, and Elisabetta Scoppola. "Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility." Electronic Journal of Probability 20 (2015). http://dx.doi.org/10.1214/ejp.v20-3656.

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Barth, Andrea, and Andreas Stein. "Numerical analysis for time-dependent advection-diffusion problems with random discontinuous coefficients." ESAIM: Mathematical Modelling and Numerical Analysis, June 10, 2022. http://dx.doi.org/10.1051/m2an/2022054.

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As an extension to the well-established stationary elliptic partial differential equation (PDE) with random continuous coefficients we study a time-dependent advection-diffusion problem, where the coefficients may have random spatial discontinuities. In a subsurface flow model, the randomness in a parabolic equation may account for insufficient measurements or uncertain material procurement, while the discontinuities could represent transitions in heterogeneous media. Specifically, a scenario with coupled advection and diffusion coefficients that are modeled as sums of continuous random fields

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Duc, Luu Hoang, and Phan Thanh Hong. "Asymptotic Dynamics of Young Differential Equations." Journal of Dynamics and Differential Equations, November 1, 2021. http://dx.doi.org/10.1007/s10884-021-10095-1.

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AbstractWe provide a unified analytic approach to study the asymptotic dynamics of Young differential equations, using the framework of random dynamical systems and random attractors. Our method helps to generalize recent results (Duc et al. in J Differ Equ 264:1119–1145, 2018, SIAM J Control Optim 57(4):3046–3071, 2019; Garrido-Atienza et al. in Int J Bifurc Chaos 20(9):2761–2782, 2010) on the existence of the global pullback attractors for the generated random dynamical systems. We also prove sufficient conditions for the attractor to be a singleton, thus the pathwise convergence is in both

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van Neerven, Jan, and Mark Veraar. "Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes." Stochastics and Partial Differential Equations: Analysis and Computations, July 10, 2021. http://dx.doi.org/10.1007/s40072-021-00204-y.

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AbstractWe prove a new Burkholder–Rosenthal type inequality for discrete-time processes taking values in a 2-smooth Banach space. As a first application we prove that if $$(S(t,s))_{0\leqslant s\le t\leqslant T}$$ ( S ( t , s ) ) 0 ⩽ s ≤ t ⩽ T is a $$C_0$$ C 0 -evolution family of contractions on a 2-smooth Banach space X and $$(W_t)_{t\in [0,T]}$$ ( W t ) t ∈ [ 0 , T ] is a cylindrical Brownian motion on a probability space $$(\Omega ,{\mathbb {P}})$$ ( Ω , P ) adapted to some given filtration, then for every $$0<p<\infty $$ 0 < p < ∞ there exists a constant $$C_{p,X}$$ C p , X su

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