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May 2021 Diffusion approximation for fully coupled stochastic differential equations
Michael Röckner, Longjie Xie
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Ann. Probab. 49(3): 1205-1236 (May 2021). DOI: 10.1214/20-AOP1475

Abstract

We consider a Poisson equation in Rd for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect to the parameter are obtained under mild conditions on the coefficients. The result is then applied to establish a general diffusion approximation for fully coupled multitime scales stochastic differential equations with only Hölder continuous coefficients. Four different averaged equations as well as rates of convergence are obtained. Moreover, the convergence is shown to rely only on the regularities of the coefficients with respect to the slow variable and does not depend on their regularities with respect to the fast component.

Citation

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Michael Röckner. Longjie Xie. "Diffusion approximation for fully coupled stochastic differential equations." Ann. Probab. 49 (3) 1205 - 1236, May 2021. https://doi.org/10.1214/20-AOP1475

Information

Received: 1 September 2019; Revised: 1 September 2020; Published: May 2021
First available in Project Euclid: 7 April 2021

Digital Object Identifier: 10.1214/20-AOP1475

Subjects:
Primary: 60H10, 60J60
Secondary: 35B30

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 3 • May 2021
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