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March 2017 Convergence and regularity of probability laws by using an interpolation method
Vlad Bally, Lucia Caramellino
Ann. Probab. 45(2): 1110-1159 (March 2017). DOI: 10.1214/15-AOP1082

Abstract

Fournier and Printems [Bernoulli 16 (2010) 343–360] have recently established a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with Hölder continuous coefficients. This is of course out of reach by using already classical probabilistic methods based on Malliavin calculus. By employing some Besov space techniques, Debussche and Romito [Probab. Theory Related Fields 158 (2014) 575–596] have substantially improved the result of Fournier and Printems. In our paper, we show that this kind of problem naturally fits in the framework of interpolation spaces: we prove an interpolation inequality (see Proposition 2.5) which allows to state (and even to slightly improve) the above absolute continuity result. Moreover, it turns out that the above interpolation inequality has applications in a completely different framework: we use it in order to estimate the error in total variance distance in some convergence theorems.

Citation

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Vlad Bally. Lucia Caramellino. "Convergence and regularity of probability laws by using an interpolation method." Ann. Probab. 45 (2) 1110 - 1159, March 2017. https://doi.org/10.1214/15-AOP1082

Information

Received: 1 June 2015; Revised: 1 October 2015; Published: March 2017
First available in Project Euclid: 31 March 2017

zbMATH: 1377.60066
MathSciNet: MR3630294
Digital Object Identifier: 10.1214/15-AOP1082

Subjects:
Primary: 46B70
Secondary: 60H07

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 2 • March 2017
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