• 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… 

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TLDR
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.
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