Stein method for invariant measures of diffusions via Malliavin calculus

Abstract

Given a random variable $F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and almost any continuous probability law on the real line. The bounds are given in terms of the Malliavin derivative of $F$. Our approach is based on the theory of Itô diffusions and the stochastic calculus of variations. Several examples are considered in order to illustrate our general results.

to appear in "Stochastic Processes and Their Applications"

References in corpus (1)

• Noncentral convergence of multiple integrals

Cited by in corpus (2)

• Stein's method of exchangeable pairs for absolutely continuous, univariate distributions with applications to the Polya urn model
• Rates of convergence towards the Fréchet distribution