Stein’s method for invariant measures of diffusions via Malliavin calculus
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 Itô diffusions and the stochastic calculus of variations. Several examples are considered in order to illustrate our general results.
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Volume (Year): 122 (2012)
Issue (Month): 4 ()
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References listed on IDEAS
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- Bo Martin Bibby, 2001. "Simplified Estimating Functions for Diffusion Models with a High-dimensional Parameter," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 99-112.
- Viens, Frederi G., 2009. "Stein's lemma, Malliavin calculus, and tail bounds, with application to polymer fluctuation exponent," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3671-3698, October.
- Yacine Ait-Sahalia, 1995.
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- Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
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