Stein's method for invariant measures of diffusions via Malliavin calculus

作者：Kusuoka Seiichiro^*; Tudor Ciprian A

来源：Stochastic Processes and Their Applications, 2012, 122(4): 1627-1651.

DOI：10.1016/j.spa.2012.02.005

• Stein's method
• Malliavin calculus
• Berry-Esseen bounds
• Weak convergence
• Multiple stochastic integrals
• Diffusions
• Invariant measure

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 any probability measure with a density function which is continuous, bounded, strictly positive on an interval in the real line and admits finite variance. The bounds are given in terms of the Malliavin derivative of F. Our approach is based on the theory of Ito diffusions and the stochastic calculus of,variations. Several examples are considered in order to illustrate our general results.

• 出版日期2012-4