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

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

Mathematics, 2023, vol. 11, issue 19, 1-23

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.

Keywords: iterated Itô stochastic integral; iterated Stratonovich stochastic integral; nonlinear stochastic dynamics; numerical method; spectral method; stochastic differential equation; Taylor–Itô expansion; Taylor–Stratonovich expansion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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