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Journal articles on the topic 'Euler Maruyama Scheme'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 April 2022

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1

Pierret, Frédéric. "A non-standard-Euler–Maruyama scheme." Journal of Difference Equations and Applications 22, no. 1 (2015): 75–98. http://dx.doi.org/10.1080/10236198.2015.1076809.

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2

Samimi, Oldouz, and Farshid Mehrdoust. "Pricing multi-asset American option under Heston stochastic volatility model." International Journal of Financial Engineering 05, no. 03 (2018): 1850026. http://dx.doi.org/10.1142/s2424786318500263.

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In this paper, we employ the Least-Squares Monte-Carlo (LSM) algorithm regarding three discretization schemes, namely, the Euler–Maruyama discretization scheme, the Milstein scheme and the Quadratic Exponential (QE) scheme to price the multiple assets American put option under the Heston stochastic volatility model. Some numerical results are presented to demonstrate the effectiveness of the proposed methods.

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3

TANAKA, HIDEYUKI, and TOSHIHIRO YAMADA. "STRONG CONVERGENCE FOR EULER–MARUYAMA AND MILSTEIN SCHEMES WITH ASYMPTOTIC METHOD." International Journal of Theoretical and Applied Finance 17, no. 02 (2014): 1450014. http://dx.doi.org/10.1142/s0219024914500149.

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Motivated by weak convergence results in the paper of Takahashi & Yoshida (2005), we show strong convergence for an accelerated Euler–Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result. The theoretical results can be applied to analyze the multi-level Monte Carlo method originally developed by M.B. Giles. Several numerical experiments for the stochastic alpha-beta-rho (SABR) model of stochastic volatility are presented in order to confirm the efficiency of the schemes.

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4

Doan, T. S., P. T. Huong, P. E. Kloeden, and A. M. Vu. "Euler–Maruyama scheme for Caputo stochastic fractional differential equations." Journal of Computational and Applied Mathematics 380 (December 2020): 112989. http://dx.doi.org/10.1016/j.cam.2020.112989.

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5

Thapa, Bharat Bahadur, Samir Shrestha, and Dil Bahadur Gurung. "Deterministic and Stochastic Holling-Tanner Prey-Predator Models." Advances in Engineering and Technology: An International Journal 1, no. 1 (2021): 1–8. http://dx.doi.org/10.3126/aet.v1i1.39604.

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A modified version of the so called Holling-Tanner prey-predator models with prey dependent functional response is introduced. We improved some new results on Holling-Tanner model from Lotka-Volterra model on real ecological systems and studied the stability of this model in the deterministic and stochastic environments. The study was focused on three types of stability, namely, stable node, spiral node, and center. The numerical schemes are employed to get the approximated solutions of the differential equations. We have used Euler scheme to solve the deterministic prey-predator model and we

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6

Kuang, Shifang, Yunjian Peng, Feiqi Deng, and Wenhua Gao. "Exponential Stability and Numerical Methods of Stochastic Recurrent Neural Networks with Delays." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/761237.

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Exponential stability in mean square of stochastic delay recurrent neural networks is investigated in detail. By using Itô’s formula and inequality techniques, the sufficient conditions to guarantee the exponential stability in mean square of an equilibrium are given. Under the conditions which guarantee the stability of the analytical solution, the Euler-Maruyama scheme and the split-step backward Euler scheme are proved to be mean-square stable. At last, an example is given to demonstrate our results.

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7

Lamba, H., J. C. Mattingly, and A. M. Stuart. "An adaptive Euler-Maruyama scheme for SDEs: convergence and stability." IMA Journal of Numerical Analysis 27, no. 3 (2006): 479–506. http://dx.doi.org/10.1093/imanum/drl032.

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8

Agrawal, Nishant, and Yaozhong Hu. "Jump Models with Delay—Option Pricing and Logarithmic Euler–Maruyama Scheme." Mathematics 8, no. 11 (2020): 1932. http://dx.doi.org/10.3390/math8111932.

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In this paper, we obtain the existence, uniqueness, and positivity of the solution to delayed stochastic differential equations with jumps. This equation is then applied to model the price movement of the risky asset in a financial market and the Black–Scholes formula for the price of European option is obtained together with the hedging portfolios. The option price is evaluated analytically at the last delayed period by using the Fourier transformation technique. However, in general, there is no analytical expression for the option price. To evaluate the price numerically, we then use the Mon

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9

Liu, Jun, and Jin Zhou. "Convergence rate of Euler–Maruyama scheme for stochastic pantograph differential equations." Communications in Nonlinear Science and Numerical Simulation 19, no. 6 (2014): 1697–705. http://dx.doi.org/10.1016/j.cnsns.2013.10.015.

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10

Yi, Yulian, Yaozhong Hu, and Jingjun Zhao. "Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations." Communications in Nonlinear Science and Numerical Simulation 101 (October 2021): 105895. http://dx.doi.org/10.1016/j.cnsns.2021.105895.

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11

Naryongo, Raphael, Philip Ngare, and Anthony Waititu. "The Log-Asset Dynamic with Euler–Maruyama Scheme under Wishart Processes." International Journal of Mathematics and Mathematical Sciences 2021 (November 25, 2021): 1–15. http://dx.doi.org/10.1155/2021/4050722.

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This article deals with Wishart process which is defined as matrix generalization of a squared Bessel process. We consider a single risky asset pricing model whose volatility is described by Wishart affine diffusion processes. The multifactor volatility specification enables this model to be flexible enough to describe the market prices for short or long maturities. The aim of the study is to derive the log-asset returns dynamic under the double Wishart stochastic volatility model. The corrected Euler–Maruyama discretization technique is applied in order to obtain the numerical solution of the

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12

Shen, Yi, and Yan Li. "Stationary in Distributions of Numerical Solutions for Stochastic Partial Differential Equations with Markovian Switching." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/752953.

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We investigate a class of stochastic partial differential equations with Markovian switching. By using the Euler-Maruyama scheme both in time and in space of mild solutions, we derive sufficient conditions for the existence and uniqueness of the stationary distributions of numerical solutions. Finally, one example is given to illustrate the theory.

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13

Naito, Riu, and Toshihiro Yamada. "A third-order weak approximation of multidimensional Itô stochastic differential equations." Monte Carlo Methods and Applications 25, no. 2 (2019): 97–120. http://dx.doi.org/10.1515/mcma-2019-2036.

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Abstract This paper proposes a new third-order discretization algorithm for multidimensional Itô stochastic differential equations driven by Brownian motions. The scheme is constructed by the Euler–Maruyama scheme with a stochastic weight given by polynomials of Brownian motions, which is simply implemented by a Monte Carlo method. The method of Watanabe distributions on Wiener space is effectively applied in the computation of the polynomial weight of Brownian motions. Numerical examples are shown to confirm the accuracy of the scheme.

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14

Baker, Christopher T. H., and Evelyn Buckwar. "Numerical Analysis of Explicit One-Step Methods for Stochastic Delay Differential Equations." LMS Journal of Computation and Mathematics 3 (2000): 315–35. http://dx.doi.org/10.1112/s1461157000000322.

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AbstractWe consider the problem of strong approximations of the solution of stochastic differential equations of Itô form with a constant lag in the argument. We indicate the nature of the equations of interest, and give a convergence proof in full detail for explicit one-step methods. We provide some illustrative numerical examples, using the Euler–Maruyama scheme.

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15

Sarhan, Falah, and LIU JICHENG. "Euler-Maruyama approximation of backward doubly stochastic differential delay equations." International Journal of Applied Mathematical Research 5, no. 3 (2016): 146. http://dx.doi.org/10.14419/ijamr.v5i3.6358.

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In this paper, we attempt to introduce a new numerical approach to solve backward doubly stochastic differential delay equation ( shortly-BDSDDEs ). In the beginning, we present some assumptions to get the numerical scheme for BDSDDEs, from which we prove important theorem. We use the relationship between backward doubly stochastic differential delay equations and stochastic controls by interpreting BDSDDEs as some stochastic optimal control problems, to solve the approximated BDSDDEs and we prove that the numerical solutions of backward doubly stochastic differential delay equation converge t

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16

Bayram, Mustafa, Buyukoz Orucova, and Tugcem Partal. "Parameter estimation in a Black Scholes." Thermal Science 22, Suppl. 1 (2018): 117–22. http://dx.doi.org/10.2298/tsci170915277b.

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In this paper we discuss parameter estimation in black scholes model. A non-parametric estimation method and well known maximum likelihood estimator are considered. Our aim is to estimate the unknown parameters for stochastic differential equation with discrete time observation data. In simulation study we compare the non-parametric method with maximum likelihood method using stochastic numerical scheme named with Euler Maruyama.

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17

Wang, Zhan Ping. "Exponential Stability of Numerical Solutions to Stochastic Investment System." Advanced Materials Research 143-144 (October 2010): 910–14. http://dx.doi.org/10.4028/www.scientific.net/amr.143-144.910.

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The investment model of stochastic neutral technical progress is given in this paper. The main purpose of this paper is to consider the exponential stability of the Euler-Maruyama scheme for a class of stochastic investment system. The de¯nition of exponential of numerical methods is established. The conditions under which the method is exponentially stable in mean square determined.

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18

Marín Sánchez, Freddy H., and J. Sebastian Palacio. "Gaussian Estimation of One-Factor Mean Reversion Processes." Journal of Probability and Statistics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/239384.

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We propose a new alternative method to estimate the parameters in one-factor mean reversion processes based on the maximum likelihood technique. This approach makes use of Euler-Maruyama scheme to approximate the continuous-time model and build a new process discretized. The closed formulas for the estimators are obtained. Using simulated data series, we compare the results obtained with the results published by other authors.

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19

BRIANI, MAYA, LUCIA CARAMELLINO, GIULIA TERENZI, and ANTONINO ZANETTE. "NUMERICAL STABILITY OF A HYBRID METHOD FOR PRICING OPTIONS." International Journal of Theoretical and Applied Finance 22, no. 07 (2019): 1950036. http://dx.doi.org/10.1142/s0219024919500365.

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We develop and study stability properties of a hybrid approximation of functionals of the Bates jump model with stochastic interest rate that uses a tree method in the direction of the volatility and the interest rate and a finite-difference approach in order to handle the underlying asset price process. We also propose hybrid simulations for the model, following a binomial tree in the direction of both the volatility and the interest rate, and a space-continuous approximation for the underlying asset price process coming from a Euler–Maruyama type scheme. We test our numerical schemes by comp

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20

Asker, Hussein K. "Well-Posedness and Exponential Estimates for the Solutions to Neutral Stochastic Functional Differential Equations with Infinite Delay." Journal of Systems Science and Information 8, no. 5 (2020): 434–46. http://dx.doi.org/10.21078/jssi-2020-434-13.

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AbstractIn this work, neutral stochastic functional differential equations with infinite delay (NSFD-EwID) have been addressed. By using the Euler-Maruyama scheme and a localization argument, the existence and uniqueness of solutions to NSFDEwID at the state space Cr under the local weak monotone condition, the weak coercivity condition and the global condition on the neutral term have been investigated. In addition, the L2 and exponential estimates of NSFDEwID have been studied.

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21

Cambams, Stamatis, and Hu Yaozhong. "Exact convergence rate of the Euler-Maruyama scheme, with application to sampling design." Stochastics and Stochastic Reports 59, no. 3-4 (1996): 211–40. http://dx.doi.org/10.1080/17442509608834090.

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22

Bao, Jianhai, Xing Huang, and Chenggui Yuan. "Convergence Rate of Euler–Maruyama Scheme for SDEs with Hölder–Dini Continuous Drifts." Journal of Theoretical Probability 32, no. 2 (2018): 848–71. http://dx.doi.org/10.1007/s10959-018-0854-9.

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23

Mao, Xuerong, Aubrey Truman, and Chenggui Yuan. "Euler-Maruyama approximations in mean-reverting stochastic volatility model under regime-switching." Journal of Applied Mathematics and Stochastic Analysis 2006 (July 13, 2006): 1–20. http://dx.doi.org/10.1155/jamsa/2006/80967.

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Stochastic differential equations (SDEs) under regime-switching have recently been developed to model various financial quantities. In general, SDEs under regime-switching have no explicit solutions, so numerical methods for approximations have become one of the powerful techniques in the valuation of financial quantities. In this paper, we will concentrate on the Euler-Maruyama (EM) scheme for the typical hybrid mean-reverting θ-process. To overcome the mathematical difficulties arising from the regime-switching as well as the non-Lipschitz coefficients, several new techniques have been devel

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24

Lu, Zhenyu, Tingya Yang, Yanhan Hu, and Junhao Hu. "Convergence Rate of Numerical Solutions for Nonlinear Stochastic Pantograph Equations with Markovian Switching and Jumps." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/420648.

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The sufficient conditions of existence and uniqueness of the solutions for nonlinear stochastic pantograph equations with Markovian switching and jumps are given. It is proved that Euler-Maruyama scheme for nonlinear stochastic pantograph equations with Markovian switching and Brownian motion is of convergence with strong order 1/2. For nonlinear stochastic pantograph equations with Markovian switching and pure jumps, it is best to use the mean-square convergence, and the order of mean-square convergence is close to 1/2.

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25

Raza, Ali, Muhammad Shoaib Arif, and Muhammad Rafiq. "A reliable numerical analysis for stochastic gonorrhea epidemic model with treatment effect." International Journal of Biomathematics 12, no. 06 (2019): 1950072. http://dx.doi.org/10.1142/s1793524519500724.

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The phenomena of disease spread are unpredictable in nature due to random mixing of individuals in a population. It is of more significance to include this randomness while modeling infectious diseases. Modeling epidemics including their stochastic behavior could be a more realistic approach in many situations. In this paper, a stochastic gonorrhea epidemic model with treatment effect has been analyzed numerically. Numerical solution of stochastic model is presented in comparison with its deterministic part. The dynamics of the gonorrhea disease is governed by a threshold quantity [Formula: se

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26

Ngo, Hoang-Long, and Dai Taguchi. "On the Euler–Maruyama scheme for SDEs with bounded variation and Hölder continuous coefficients." Mathematics and Computers in Simulation 161 (July 2019): 102–12. http://dx.doi.org/10.1016/j.matcom.2019.01.012.

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27

Müller-Gronbach, Thomas, and Larisa Yaroslavtseva. "On the performance of the Euler–Maruyama scheme for SDEs with discontinuous drift coefficient." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 56, no. 2 (2020): 1162–78. http://dx.doi.org/10.1214/19-aihp997.

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28

Guo, Qian, Wei Liu, Xuerong Mao, and Weijun Zhan. "Multi-level Monte Carlo methods with the truncated Euler–Maruyama scheme for stochastic differential equations." International Journal of Computer Mathematics 95, no. 9 (2017): 1715–26. http://dx.doi.org/10.1080/00207160.2017.1329533.

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29

Liu, Linna, Mengling Li, and Feiqi Deng. "Stability equivalence between the neutral delayed stochastic differential equations and the Euler–Maruyama numerical scheme." Applied Numerical Mathematics 127 (May 2018): 370–86. http://dx.doi.org/10.1016/j.apnum.2018.01.016.

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30

Haiek, Mohammed, Youness El Ansari, Nabil Ben Said Amrani, and Driss Sarsri. "A Stochastic Model of Stress Evolution in a Bolted Structure in the Presence of a Joint Elastic Piece: Modeling and Parameter Inference." Advances in Materials Science and Engineering 2020 (October 30, 2020): 1–11. http://dx.doi.org/10.1155/2020/9601212.

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In this paper, we propose a stochastic model to describe over time the evolution of stress in a bolted mechanical structure depending on different thicknesses of a joint elastic piece. First, the studied structure and the experiment numerical simulation are presented. Next, we validate statistically our proposed stochastic model, and we use the maximum likelihood estimation method based on Euler–Maruyama scheme to estimate the parameters of this model. Thereafter, we use the estimated model to compare the stresses, the peak times, and extinction times for different thicknesses of the elastic p

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31

Romero-Melendez, Cutberto, and David Castillo-Fernandez. "A stochastic controlled Schroedinger equation: convergence and robust stability for numerical solutions." Cybernetics and Physics, Volume 10, 2021, Number 3 (November 30, 2021): 178–84. http://dx.doi.org/10.35470/2226-4116-2021-10-3-178-184.

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In this paper we study the stochastic stability of numerical solutions of a stochastic controlled Schr¨odinger equation. We investigate the boundedness in second moment, the convergence and the stability of the zero solution for this equation, using two new definitions of almost sure exponential robust stability and asymptotic stability, for the Euler-Maruyama numerical scheme. Considering that the diffusion term is controlled, by using the method of Lyapunov functions and the corresponding diffusion operator associated, we apply techniques of X. Mao and A. Tsoi for achieve our task. Finally,

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32

Chen, Lin, and Fu Ke Wu. "Almost Sure Decay Stability of the Backward Euler-Maruyama Scheme for Stochastic Differential Equations with Unbounded Delay." Applied Mechanics and Materials 235 (November 2012): 39–44. http://dx.doi.org/10.4028/www.scientific.net/amm.235.39.

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This paper deals with analytical and numerical stability properties of highly nonlinear stochastic differential equations (SDEs) with unbounded delay. Sufficient conditions for almost sure decay stability of previous system, almost sure decay stability of the backward Euler-Maruyama (BEM) methods are investigated. In \cite{Wu2010} and \cite{Mao2011}, the authors consider one-side linear growth condition and sufficient small step size. In this paper, we consider the monotone condition, which is weaker than one-side linear growth condition. And we only need a very weak restriction of the step si

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33

Li, Libo, and Dai Taguchi. "On the Euler–Maruyama scheme for spectrally one-sided Lévy driven SDEs with Hölder continuous coefficients." Statistics & Probability Letters 146 (March 2019): 15–26. http://dx.doi.org/10.1016/j.spl.2018.10.017.

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34

Neuenkirch, Andreas, Michaela Szölgyenyi, and Lukasz Szpruch. "An Adaptive Euler--Maruyama Scheme for Stochastic Differential Equations with Discontinuous Drift and its Convergence Analysis." SIAM Journal on Numerical Analysis 57, no. 1 (2019): 378–403. http://dx.doi.org/10.1137/18m1170017.

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35

Lord, Gabriel J., and Antoine Tambue. "A modified semi–implicit Euler–Maruyama scheme for finite element discretization of SPDEs with additive noise." Applied Mathematics and Computation 332 (September 2018): 105–22. http://dx.doi.org/10.1016/j.amc.2018.03.014.

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36

Oyuna, Dondukova, and Liu Yaobin. "Forecasting the Crude Oil Prices Volatility With Stochastic Volatility Models." SAGE Open 11, no. 3 (2021): 215824402110262. http://dx.doi.org/10.1177/21582440211026269.

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In this article, the stochastic volatility model is introduced to forecast crude oil volatility by using data from the West Texas Intermediate (WTI) and Brent markets. Not only that the model can capture stylized facts of multiskilling, extended memory, and structural breaks in volatility, it is also more frugal in parameterizations. The Euler–Maruyama scheme was applied to approximate the Heston model. On the contrary, the root mean square error (RMSE) and the mean average error (MAE) were used to approximate the generalized autoregressive conditional heteroskedasticity (GARCH)–type models (s

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37

Halidias, Nikolaos, and Peter E. Kloeden. "A note on the Euler–Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient." BIT Numerical Mathematics 48, no. 1 (2008): 51–59. http://dx.doi.org/10.1007/s10543-008-0164-1.

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38

Kohatsu-Higa, Arturo, Antoine Lejay, and Kazuhiro Yasuda. "Weak rate of convergence of the Euler–Maruyama scheme for stochastic differential equations with non-regular drift." Journal of Computational and Applied Mathematics 326 (December 2017): 138–58. http://dx.doi.org/10.1016/j.cam.2017.05.015.

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39

Li, Yan, Ming Ye, and Qimin Zhang. "Strong convergence of the partially truncated Euler–Maruyama scheme for a stochastic age-structured SIR epidemic model." Applied Mathematics and Computation 362 (December 2019): 124519. http://dx.doi.org/10.1016/j.amc.2019.06.033.

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40

Zhou, Shaobo. "Strong convergence and stability of backward Euler–Maruyama scheme for highly nonlinear hybrid stochastic differential delay equation." Calcolo 52, no. 4 (2014): 445–73. http://dx.doi.org/10.1007/s10092-014-0124-x.

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41

Akahori, Jirô, Masahiro Kinuya, Takashi Sawai, and Tomooki Yuasa. "An efficient weak Euler–Maruyama type approximation scheme of very high dimensional SDEs by orthogonal random variables." Mathematics and Computers in Simulation 187 (September 2021): 540–65. http://dx.doi.org/10.1016/j.matcom.2021.03.010.

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42

Siying, QIAN, ZHANG Jingna, and HUANG Jianfei. "A Modified Euler-Maruyama Scheme for Multi-Term Fractional Nonlinear Stochastic Differential Equations With Weakly Singular Kernels." 应用数学和力学 42, no. 11 (2021): 1203–12. http://dx.doi.org/10.21656/1000-0887.420067.

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43

Rajivganthi, Chinnathambi, and Fathalla A. Rihan. "Global Dynamics of a Stochastic Viral Infection Model with Latently Infected Cells." Applied Sciences 11, no. 21 (2021): 10484. http://dx.doi.org/10.3390/app112110484.

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In this paper, we study the global dynamics of a stochastic viral infection model with humoral immunity and Holling type II response functions. The existence and uniqueness of non-negative global solutions are derived. Stationary ergodic distribution of positive solutions is investigated. The solution fluctuates around the equilibrium of the deterministic case, resulting in the disease persisting stochastically. The extinction conditions are also determined. To verify the accuracy of the results, numerical simulations were carried out using the Euler–Maruyama scheme. White noise’s intensity pl

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44

Pieschner, Susanne, and Christiane Fuchs. "Bayesian inference for diffusion processes: using higher-order approximations for transition densities." Royal Society Open Science 7, no. 10 (2020): 200270. http://dx.doi.org/10.1098/rsos.200270.

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Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods that introduce auxiliary data. These methods typically approximate the transition densities of the process numerically, both for calculating the posterior densities and proposing auxiliary data. Here, the Euler–Maruyama scheme is the standard approximation technique. However, the MCMC method is computationally expensive. Using higher-order approximations ma

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45

Harang, Fabian A., Marc Lagunas-Merino, and Salvador Ortiz-Latorre. "Self-exciting multifractional processes." Journal of Applied Probability 58, no. 1 (2021): 22–41. http://dx.doi.org/10.1017/jpr.2020.88.

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AbstractWe propose a new multifractional stochastic process which allows for self-exciting behavior, similar to what can be seen for example in earthquakes and other self-organizing phenomena. The process can be seen as an extension of a multifractional Brownian motion, where the Hurst function is dependent on the past of the process. We define this by means of a stochastic Volterra equation, and we prove existence and uniqueness of this equation, as well as giving bounds on the p-order moments, for all $p\geq1$. We show convergence of an Euler–Maruyama scheme for the process, and also give th

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46

Rihan, Fathalla A., and Chinnathambi Rajivganthi. "Dynamics of Tumor-Immune System with Random Noise." Mathematics 9, no. 21 (2021): 2707. http://dx.doi.org/10.3390/math9212707.

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With deterministic differential equations, we can understand the dynamics of tumor-immune interactions. Cancer-immune interactions can, however, be greatly disrupted by random factors, such as physiological rhythms, environmental factors, and cell-to-cell communication. The present study introduces a stochastic differential model in infectious diseases and immunology of the dynamics of a tumor-immune system with random noise. Stationary ergodic distribution of positive solutions to the system is investigated in which the solution fluctuates around the equilibrium of the deterministic case and

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47

Chen, Lin, and Fuke Wu. "Almost sure exponential stability of the backward Euler–Maruyama scheme for stochastic delay differential equations with monotone-type condition." Journal of Computational and Applied Mathematics 282 (July 2015): 44–53. http://dx.doi.org/10.1016/j.cam.2014.12.036.

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48

Banchuin, Rawid, and Roungsan Chaisricharoen. "Vector SDE Based Stochastic Analysis of Transformer." ECTI Transactions on Computer and Information Technology (ECTI-CIT) 15, no. 1 (2021): 82–107. http://dx.doi.org/10.37936/ecti-cit.2021151.188931.

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In this research, the stochastic behaviours oftransformer have been analysed by using the stochasticdifferential equation approach where both noise in thevoltage source applied to the transformer and the randomvariations in elements and parameters of transformers havebeen considered. The resulting vector stochasticdifferential equations of the transformer have been bothanalytically and numerically solved in the Ito sense wherethe Euler-Maruyama scheme has been adopted fordetermining the numerical solutions which have been theirsample means have been used for verification. With theobtained anal

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49

Romero-Meléndez, Cutberto, David Castillo-Fernández, and Leopoldo González-Santos. "On the Boundedness of the Numerical Solutions’ Mean Value in a Stochastic Lotka–Volterra Model and the Turnpike Property." Complexity 2021 (October 22, 2021): 1–14. http://dx.doi.org/10.1155/2021/4445496.

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In this paper, we study some properties of the solutions of a stochastic Lotka–Volterra predator-prey model, namely, the boundedness in the mean of numerical solutions, the strong convergence for this kind of solutions, and the turnpike property of solutions of an optimal control problem in a population modelled by a Lotka–Volterra system with stochastic environmental fluctuations. Even though there are numerous results in the deterministic case, there are few results for the behavior of numerical solutions in a population dynamic with random fluctuations. First, we show, using the Euler–Maruy

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Li, Xingjie Helen, Fei Lu, and Felix X. F. Ye. "ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems." Discrete & Continuous Dynamical Systems - S 15, no. 4 (2022): 747. http://dx.doi.org/10.3934/dcdss.2021103.

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Abstract:

<p style='text-indent:20px;'>Efficient simulation of SDEs is essential in many applications, particularly for ergodic systems that demand efficient simulation of both short-time dynamics and large-time statistics. However, locally Lipschitz SDEs often require special treatments such as implicit schemes with small time-steps to accurately simulate the ergodic measures. We introduce a framework to construct inference-based schemes adaptive to large time-steps (ISALT) from data, achieving a reduction in time by several orders of magnitudes. The key is the statistical learning of an approxim

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