stochastic differential

diffusion equation

option pricing

fractional brownian

ornstein uhlenbeck

propagation chaos

stochastic approximation

stochastic flows

stochastic partial

diffusion processes

Annals of Probability

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.

Diffusion approximation for fully coupled stochastic differential equations