Strong approximation rate for Wiener process by fast oscillating integrated Ornstein–Uhlenbeck processes

Junlin Li, Hongbo Fu, Ziying He and Yiwei Zhang

Chaos, Solitons & Fractals, 2018, vol. 113, issue C, 314-325

Abstract: In this paper, we use fast oscillating integrated Ornstein–Uhlenbeck (abbreviated as O-U) processes to pathwisely approximate Wiener processes. In physics, such approximation process is known as a colored noise approximation, and is suitable for dealing with stochastic flow problems. Our first result shows that if the drift term of a stochastic differential equation (abbreviated as SDE) satisfies usual Lipschitz constrains and a linear growth condition, then the solution of the SDE can be almost surely approximated with a polynomial rate. Next, we explore the O-U process approximation on the random manifold of stochastic evolution equations with linear multiplicative noise. Our second result shows that if the stochastic evolution equation further satisfies a uniformly hyperbolic condition, then the corresponding random manifold approximation also converges almost surely, with a polynomial rate.

Keywords: Integrated Ornstein–Uhlenbeck processes; Pathwise approximation for stochastic differential equations; Stochastic evolution equations; Approximation of random invariant manifolds (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:113:y:2018:i:c:p:314-325

DOI: 10.1016/j.chaos.2018.05.019

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