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Corpus ID: 238583172

Wong--Zakai approximations with convergence rate for stochastic differential equations with regime switching

@inproceedings{Nguyen2021WongZakaiAW,
title={Wong--Zakai approximations with convergence rate for stochastic differential equations with regime switching},
author={Giang T. Nguyen and Oscar Peralta},
year={2021}
}

We construct Wong–Zakai approximations of time–inhomogeneous stochastic differential equations with regime switching (RSSDEs), and provide a convergence rate. In the proposed approximations, the standard Brownian motion driving the time-inhomogeneous RSSDEs is replaced by a family of finite– variation processes {F}λ>0. We show that if Fλ strongly converges to B at rate δ(λ), then the Wong–Zakai approximation strongly converges to the original solution of the time–inhomogeneous RSSDE at rate… Expand

Introduction
1 Stochastic Integration in M-type 2 Banach Spaces
2 Approximations of SDEs with Lipschitz and bounded coefficients
3 Approximation of SDEs whose coefficients are locally… Expand

The author's results are preceded by the introduction of two new forms of correction terms in infinite dimensions appearing in the Wong-Zakai approximations, and these results are divided into four parts: for stochastic delay equations, for semilinear and nonlinear Stochastic equations in abstract spaces, and for the Navier-Stokes equations.Expand

A rate of convergence of a sequence of uniform transport processes to Brownian motion is derived, and a correspondmg rate for the Wong and Zakai approximation of stochastic integrals is given