Relevant bibliographies by topics / Stochastic Difference Equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Stochastic Difference Equation'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Stochastic Difference Equation"

1

S., Elizabeth, and Nirmal Veena S. "STABILIZATION OF DISCRETE STOCHASTIC DYNAMIC SYSTEM WITH DELAY." International Journal of Current Research and Modern Education, Special Issue (August 13, 2017): 53–56. https://doi.org/10.5281/zenodo.842234.

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In this paper, we discuss the stability of stochastic type differential equations through obtaining the stability condition for the respective stochastic difference equation. The system formulation is done by considering the stochastic differential equation that describes the dynamics of single isolated neuron involving delay. Here the discretization of the stochastic differential equation is done through the Euler- Maruyama Method. And the desired stability is obtained by applying suitable assumptions and through the help of theorems. The obtained theoretical results are represented through n
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Ding, Xiaohua. "Exponential stability of a kind of stochastic delay difference equations." Discrete Dynamics in Nature and Society 2006 (2006): 1–9. http://dx.doi.org/10.1155/ddns/2006/94656.

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We present a Razumilchin-type theorem for stochastic delay difference equation, and use it to investigate the mean square exponential stability of a kind of nonautonomous stochastic difference equation which may also be viewed as an approximation of a nonautonomous stochastic delay integrodifferential equations (SDIDEs), and of a difference equation arises from some of the earliest mathematical models of the macroeconomic “trade cycle” with the environmental noise.
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Galal, O. H. "A Proposed Stochastic Finite Difference Approach Based on Homogenous Chaos Expansion." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/950469.

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This paper proposes a stochastic finite difference approach, based on homogenous chaos expansion (SFDHC). The said approach can handle time dependent nonlinear as well as linear systems with deterministic or stochastic initial and boundary conditions. In this approach, included stochastic parameters are modeled as second-order stochastic processes and are expanded using Karhunen-Loève expansion, while the response function is approximated using homogenous chaos expansion. Galerkin projection is used in converting the original stochastic partial differential equation (PDE) into a set of coupled
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Allen, E. J. "Stochastic difference equations and a stochastic partial differential equation for neutron transport." Journal of Difference Equations and Applications 18, no. 8 (2012): 1267–85. http://dx.doi.org/10.1080/10236198.2010.488229.

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Abdallah, Lallouche, Aoufi Amani, and Tedjine Meriem. "Stability of equilibrium states for a stochastic difference equation of exponential form." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 2 (2024): e6475. http://dx.doi.org/10.54021/seesv5n2-080.

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It is well know that many process and problems in different fields of sciences and engineering can be modelled by linear and nonlinear difference equations. Particularly, in case of systems biology, ecology, biochemistry, genetics and physiology dynamics, many population models are governed by exponential difference equations, and lot of papers were published in this matter. The goal of this work is to study a nonlinear second order difference equation of exponential form: Xn+1 = bXn + cXne−σXn−1, n ≥ 0 where the parameters b, c have arbitrary values, σ > 0 and the initial values, X0, X−1 a
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SHAIKHET, LEONID. "GENERAL METHOD OF LYAPUNOV FUNCTIONALS CONSTRUCTION IN STABILITY INVESTIGATIONS OF NONLINEAR STOCHASTIC DIFFERENCE EQUATIONS WITH CONTINUOUS TIME." Stochastics and Dynamics 05, no. 02 (2005): 175–88. http://dx.doi.org/10.1142/s0219493705001377.

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The general method of Lyapunov functionals construction has been developed during the last decade for stability investigations of stochastic differential equations with after-effect and stochastic difference equations. After some modification of the basic Lyapunov type theorem this method was successfully used also for difference Volterra equations with continuous time. The latter often appear as useful mathematical models. Here this method is used for a stability investigation of some nonlinear stochastic difference equation with continuous time.
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A. Lallouche. "Stability Of Equilibrium States For A Stochastically Perturbed Pielou’s Equation [." Communications on Applied Nonlinear Analysis 31, no. 7s (2024): 631–40. http://dx.doi.org/10.52783/cana.v31.1403.

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It is widely recognized that the theory of stochastic difference equations is a mathematical area of great interest. Concrete systems and processes is one of its subareas, which is of some interest nowadays. Specifically, in fields such as systems biology, ecology, biochemistry, genetics, and physiology dynamics, numerous population models are described by studying linear and nonlinear difference equations and systems. These studies have been very productive and helpful to develop the basic theory of the qualitative behaviour of nonlinear rational and exponential difference equations and syste
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Ungureanu, Viorica Mariela, and Sui Sun Cheng. "Mean stability of a stochastic difference equation." Annales Polonici Mathematici 93, no. 1 (2008): 33–52. http://dx.doi.org/10.4064/ap93-1-3.

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KUSKE, R., and J. B. KELLER. "Large deviation theory for stochastic difference equations." European Journal of Applied Mathematics 8, no. 6 (1997): 567–80. http://dx.doi.org/10.1017/s095679259700332x.

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The probability density for the solution yn of a stochastic difference equation is considered. Following Knessl et al. [1], it is shown to satisfy a master equation, which is solved asymptotically for large values of the index n. The method is illustrated by deriving the large deviation results for a sum of independent identically distributed random variables and for the joint density of two dependent sums. Then it is applied to a difference approximation to the Helmholtz equation in a random medium. A large deviation result is obtained for the probability density of the decay rate of a soluti
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Wu, Kaining, Xiaohua Ding, and Liming Wang. "Stability and Stabilization of Impulsive Stochastic Delay Difference Equations." Discrete Dynamics in Nature and Society 2010 (2010): 1–15. http://dx.doi.org/10.1155/2010/592036.

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When an impulsive control is adopted for a stochastic delay difference system (SDDS), there are at least two situations that should be contemplated. If the SDDS is stable, then what kind of impulse can the original system tolerate to keep stable? If the SDDS is unstable, then what kind of impulsive strategy should be taken to make the system stable? Using the Lyapunov-Razumikhin technique, we establish criteria for the stability of impulsive stochastic delay difference equations and these criteria answer those questions. As for applications, we consider a kind of impulsive stochastic delay dif
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Dissertations / Theses on the topic "Stochastic Difference Equation"

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Shedlock, Andrew James. "A Numerical Method for solving the Periodic Burgers' Equation through a Stochastic Differential Equation." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/103947.

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The Burgers equation, and related partial differential equations (PDEs), can be numerically challenging for small values of the viscosity parameter. For example, these equations can develop discontinuous solutions (or solutions with large gradients) from smooth initial data. Aside from numerical stability issues, standard numerical methods can also give rise to spurious oscillations near these discontinuities. In this study, we consider an equivalent form of the Burgers equation given by Constantin and Iyer, whose solution can be written as the expected value of a stochastic differential eq
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Redmon, Jessica. "Stochastic Bubble Formation and Behavior in Non-Newtonian Fluids." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case15602738261697.

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Zhou, Bo. "The existence of bistable stationary solutions of random dynamical systems generated by stochastic differential equations and random difference equations." Thesis, Loughborough University, 2009. https://dspace.lboro.ac.uk/2134/14255.

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In this thesis, we study the existence of stationary solutions for two cases. One is for random difference equations. For this, we prove the existence and uniqueness of the stationary solutions in a finite-dimensional Euclidean space Rd by applying the coupling method. The other one is for semi linear stochastic evolution equations. For this case, we follows Mohammed, Zhang and Zhao [25]'s work. In an infinite-dimensional Hilbert space H, we release the Lipschitz constant restriction by using Arzela-Ascoli compactness argument. And we also weaken the globally bounded condition for F by applyin
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Zanchini, Giulia. "Stochastic local volatility model for fx markets." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7685/.

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Questa tesi verte sullo studio di un modello a volatilità stocastica e locale, utilizzato per valutare opzioni esotiche nei mercati dei cambio. La difficoltà nell'implementare un modello di tal tipo risiede nella calibrazione della leverage surface e uno degli scopi principali di questo lavoro è quello di mostrarne la procedura.
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Challa, Subhash. "Nonlinear state estimation and filtering with applications to target tracking problems." Thesis, Queensland University of Technology, 1998.

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Čajánek, Michal. "Modely stochastického programování v inženýrském návrhu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2009. http://www.nusl.cz/ntk/nusl-228544.

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Two-stage stochastic programming problem with PDE constraint, specially elliptic equation is formulated. The computational scheme is proposed, whereas the emphasis is put on approximation techniques. We introduce method of approximation of random variables of stochastic problem and utilize suitable numerical methods, finite difference method first, then finite element method. There is also formulated a mathematical programming problem describing a membrane deflection with random load. It is followed by determination of the acceptableness of using stochastic optimization rather than determinist
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Jeisman, Joseph Ian. "Estimation of the parameters of stochastic differential equations." Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16205/1/Joseph_Jesiman_Thesis.pdf.

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Stochastic di®erential equations (SDEs) are　central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the　instantaneous short-term interest rate, asset prices, asset returns and their volatility.　The explanatory and/or predictive power of these models depends crucially on the particularisation of the model SDE(s) to real data through the choice of values for their parameters. In econometrics, optimal parameter estimates are generally considered to　be those that maximise the likelihood of the sample. In the context of the estimation of
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Jeisman, Joseph Ian. "Estimation of the parameters of stochastic differential equations." Queensland University of Technology, 2006. http://eprints.qut.edu.au/16205/.

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Stochastic di®erential equations (SDEs) are　central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the　instantaneous short-term interest rate, asset prices, asset returns and their volatility.　The explanatory and/or predictive power of these models depends crucially on the particularisation of the model SDE(s) to real data through the choice of values for their parameters. In econometrics, optimal parameter estimates are generally considered to　be those that maximise the likelihood of the sample. In the context of the estimation of t
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Antar, Ezequiel. "Risk measures and financial innovation with backward stochastic difference/differential equations." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708320.

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Roth, Jacob M. "The Explicit Finite Difference Method: Option Pricing Under Stochastic Volatility." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/cmc_theses/545.

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This paper provides an overview of the finite difference method and its application to approximating financial partial differential equations (PDEs) in incomplete markets. In particular, we study German’s [6] stochastic volatility PDE derived from indifference pricing. In [6], it is shown that the first order- correction to derivatives valued by indifference pricing can be computed as a function involving the stochastic volatility PDE itself. In this paper, we present three explicit finite difference models to approximate the stochastic volatility PDE and compare the resulting valuations to th
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Books on the topic "Stochastic Difference Equation"

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Csiszár, Imre, and György Michaletzky. Stochastic Differential and Difference Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-1980-4.

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Csiszár, Imre. Stochastic Differential and Difference Equations. Birkhäuser Boston, 1997.

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1938-, Csiszár Imre, Michaletzky György 1950-, and Conference on Stochastic Differential and Difference Equations (1996 : Győr, Hungary), eds. Stochastic differential and difference equations. Birkhäuser, 1997.

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Abadir, Karim M. Bias nonmonotonicity in stochastic difference equations. University of Exeter, Department of Economics, 1995.

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Shaikhet, Leonid. Optimal Control of Stochastic Difference Volterra Equations. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-13239-6.

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6

Shaĭkhet, L. E. Lyapunov functionals and stability of stochastic difference equations. Springer, 2011.

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Shaikhet, Leonid. Lyapunov Functionals and Stability of Stochastic Difference Equations. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-685-6.

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Korenevskiĭ, D. G. Ustoĭchivostʹ resheniĭ determinirovannykh i stokhasticheskikh different͡s︡ialʹno-raznostnykh uravneniĭ: Algebraicheskie kriterii. Naukova dumka, 1992.

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9

Friz, Peter K. Multidimensional stochastic processes as rough paths: Theory and applications. Cambridge University Press, 2010.

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Friz, Peter K. Multidimensional stochastic processes as rough paths: Theory and applications. Cambridge University Press, 2010.

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Book chapters on the topic "Stochastic Difference Equation"

1

Fukushima, Masatoshi. "Dirichlet Forms, Caccioppoli Sets and the Skorohod Equation." In Stochastic Differential and Difference Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-1980-4_6.

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Cruzeiro, A. B., and Z. Haba. "Invariant Measure for a Wave Equation on a Riemannian Manifold." In Stochastic Differential and Difference Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-1980-4_4.

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Sipin, Alexander S., and Andrey N. Kuznetsov. "On Some Stochastic Algorithms for the Numerical Solution of the First Boundary Value Problem for the Heat Equation." In Differential and Difference Equations with Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56323-3_11.

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Pichler, L., A. Masud, and L. A. Bergman. "Numerical Solution of the Fokker–Planck Equation by Finite Difference and Finite Element Methods—A Comparative Study." In Computational Methods in Stochastic Dynamics. Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5134-7_5.

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Elber, Ron, Avijit Ghosh, and Alfredo Cárdenas. "The Stochastic Difference Equation as a Tool to Compute Long Time Dynamics." In Bridging Time Scales: Molecular Simulations for the Next Decade. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45837-9_12.

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Chernogorova, Tatiana, and Radoslav Valkov. "Finite-Volume Difference Scheme for the Black-Scholes Equation in Stochastic Volatility Models." In Numerical Methods and Applications. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18466-6_45.

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Koller, Michael. "Difference Equations and Differential Equations." In Stochastic Models in Life Insurance. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28439-7_5.

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Spectorsky, Igor. "Stochastic Equations in Formal Mappings." In Stochastic Differential and Difference Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-1980-4_20.

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Shaikhet, Leonid. "Difference Equations as Difference Analogues of Differential Equations." In Lyapunov Functionals and Stability of Stochastic Difference Equations. Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-685-6_10.

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Boshnakov, Georgi N. "Periodically Correlated Solutions to a Class of Stochastic Difference Equations." In Stochastic Differential and Difference Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-1980-4_1.

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Conference papers on the topic "Stochastic Difference Equation"

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Zeng, Junshan, Yao Lin, Zheng Yu, and Yabo Wang. "The almost everywhere oscillations of a second-order stochastic difference equation." In International Conference on Modern Engineering Soultions for the Industry. WIT Press, 2014. http://dx.doi.org/10.2495/mesi141772.

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Priya, G. Vinu, and R. Jothilakshmi. "Extended Kalman filter techniques and difference equation for time varying stochastic nonlinearities." In INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS, COMPUTING AND COMMUNICATION TECHNOLOGIES: (ICAMCCT 2021). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0070779.

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Ashyralyev, Allaberen, and Ulker Okur. "Crank-Nicholson difference scheme for a stochastic parabolic equation with a dependent operator coefficient." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959717.

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Ratchagit, Manlika, Benchawan Wiwatanapataphee, and Darfiana Nur. "On Parameter Estimation of Stochastic Delay Difference Equation using the Two $m$-delay Autoregressive Coefficients." In 2020 3rd International Seminar on Research of Information Technology and Intelligent Systems (ISRITI). IEEE, 2020. http://dx.doi.org/10.1109/isriti51436.2020.9315414.

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Sinha, Prawal, and Getachew Adamu. "Thermal and Roughness Effects in a Slider Bearing Considering Conduction Through Both the Pad and the Slider." In STLE/ASME 2008 International Joint Tribology Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/ijtc2008-71023.

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This paper analyses the thermal and roughness effects on different characteristics of an infinitely long tilted pad slider bearing considering heat conduction through both the pad and slider. The roughness is assumed to be stochastic, Gaussian randomly distributed. Density and viscosity are assumed to be temperature dependent. The irregular domain of the fluid due to roughness is mapped to a regular domain so that the numerical method can be easily applied. The modified Reynolds equation, momentum equation, continuity equation, energy equation and the heat conduction equations on the pad and s
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Olawale, Lukman, Erwin George, Tao Gao, and Choi-Hong Lai. "Response of a slender structure subject to stochastic ground motion and body force." In UK Association for Computational Mechanics Conference 2024. Durham University, 2024. http://dx.doi.org/10.62512/conf.ukacm2024.076.

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The stochastic analysis of the deflection behaviour of an idealised slender structure subject to stochastic disturbance is studied. In a previous work by the authors, the response of an Euler-Bernoulli beam subject to stochastic disturbance was studied. The current work extends the same techniques to a modified Euler-Bernoulli beam with both flexural beam and shear properties. The beam is subjected to a stochastic ground motion in the form of periodic motion with disturbance in the amplitude of the motion. The disturbance is in the form of Gaussian white noise. This results in a Stochastic Par
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Zeng, Junshan, Sufang Han, Yao Lin та Zheng Yu. "The almost everywhere oscillations of the stochastic difference equation Δ2x(n) +f(n)F(x(n)) =ξ(n+ 2)". У International Conference on Modern Engineering Soultions for the Industry. WIT Press, 2014. http://dx.doi.org/10.2495/mesi141762.

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Aberkane, Samir, and Vasile Dragan. "On a solution to the problem of time-varying zero-sum LQ stochastic difference game: A Riccati equation approach." In 2019 18th European Control Conference (ECC). IEEE, 2019. http://dx.doi.org/10.23919/ecc.2019.8795655.

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Kakkar, Deepti, Aditi Bharmaik, Ankita Sharma, Eshwari S. S. Dagar, Parul Rattanpal, and Shefali Sharma. "Hata Model Path Loss Optimization using Least Mean Square Regression." In International Conference on Women Researchers in Electronics and Computing. AIJR Publisher, 2021. http://dx.doi.org/10.21467/proceedings.114.34.

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Astochastic approach based optimization technique to optimize the Hata model path loss equation is presented in this paper. In this paper, the existing Hata model equation for determining path loss in medium urban city is optimized using Least Mean Square regression method. Out of various path loss models available, Hata model was chosen due to its accuracy and reliability in an urban propagation environment. The optimization technique proposed is applied to get the optimumcoefficients of Hata propagation model equation. This stochastic approach is based on reducing the mean square difference
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Appleby, J. A. D., G. Berkolaiko, and A. Rodkina. "Non-Exponential Stability and Decay Rates in Nonlinear Stochastic Homogeneous Difference Equations." In Proceedings of the Twelfth International Conference on Difference Equations and Applications. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814287654_0008.

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Reports on the topic "Stochastic Difference Equation"

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Russo, David, and William A. Jury. Characterization of Preferential Flow in Spatially Variable Unsaturated Field Soils. United States Department of Agriculture, 2001. http://dx.doi.org/10.32747/2001.7580681.bard.

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Preferential flow appears to be the rule rather than the exception in field soils and should be considered in the quantitative description of solute transport in the unsaturated zone of heterogeneous formations on the field scale. This study focused on both experimental monitoring and computer simulations to identify important features of preferential flow in the natural environment. The specific objectives of this research were: (1) To conduct dye tracing and multiple tracer experiments on undisturbed field plots to reveal information about the flow velocity, spatial prevalence, and time evol
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