Stein’s method for invariant measures of diffusions via Malliavin calculus☆
By S. Kusuoka, Ciprian A. Tudor. 2012
52 citations recorded by the source corpus.
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.
Subfields: Finance, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/57d70a6124f9650b230e64cc4469fe366381759f
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Citations in the corpus
- Stein's method for comparison of univariate distributions (2014, methodology): “3 Invariant measures of diffusions Recent papers [28, 54, 55] provide a general framework for performing Stein’s method with respect to densities p which are supposed to admit a variance and be continuous (with respect to the Lebesgue measure), bounded with open interval support.”
- Approximation of stable law in Wasserstein-1 distance by Stein’s method (2017, methodology): “Nowadays, Stein’s method has been extended and refined by many authors and become a very important tool for getting bounds of measure approximations, see [6, 10, 14, 22, 24, 29, 39, 46, 26, 27, 28, 33, 42, 43, 44, 47].”