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Spectral Representations of Iterated Stochastic Integrals and Their Application for Modeling Nonlinear Stochastic Dynamics

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  • Konstantin Rybakov

    (Department of Mathematical Cybernetics, Moscow Aviation Institute (National Research University), 125993 Moscow, Russia)

Abstract

Spectral representations of iterated Itô and Stratonovich stochastic integrals of arbitrary multiplicity, including integrals from Taylor–Itô and Taylor–Stratonovich expansions, are obtained by the spectral method. They are required for the implementation of numerical methods for solving Itô and Stratonovich stochastic differential equations with high orders of mean-square and strong convergence. The purpose of such numerical methods is the modeling of nonlinear stochastic dynamics in many fields. This paper contains necessary theoretical results, as well as the results of numerical experiments.

Suggested Citation

  • Konstantin Rybakov, 2023. "Spectral Representations of Iterated Stochastic Integrals and Their Application for Modeling Nonlinear Stochastic Dynamics," Mathematics, MDPI, vol. 11(19), pages 1-23, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4047-:d:1246607
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    References listed on IDEAS

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    1. Yoshihiro Saito & Taketomo Mitsui, 1993. "Simulation of stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 419-432, September.
    2. Xingtong Liu & Yuanshun Tan & Bo Zheng, 2022. "Dynamic Behavior of an Interactive Mosquito Model under Stochastic Interference," Mathematics, MDPI, vol. 10(13), pages 1-18, June.
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    Cited by:

    1. Tatyana Averina, 2024. "Conditional Optimization of Algorithms for Estimating Distributions of Solutions to Stochastic Differential Equations," Mathematics, MDPI, vol. 12(4), pages 1-16, February.

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