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2014 On the distances between probability density functions
Vlad Bally, Lucia Caramellino
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Electron. J. Probab. 19(none): 1-33 (2014). DOI: 10.1214/EJP.v19-3175

Abstract

We give estimates of the distance between the densities of the laws of two functionals $F$ and $G$ on the Wiener space in terms of the Malliavin-Sobolev norm of $F-G.$ We actually consider a more general framework which allows one to treat with similar (Malliavin type)methods functionals of a Poisson point measure (solutions of jump type stochastic equations). We use the above estimates in order to obtain a criterion which ensures that convergence in distribution implies convergence in total variation distance; in particular, if the functionals at hand are absolutely continuous, this implies convergence in $L^{1}$ of the densities.

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Vlad Bally. Lucia Caramellino. "On the distances between probability density functions." Electron. J. Probab. 19 1 - 33, 2014. https://doi.org/10.1214/EJP.v19-3175

Information

Accepted: 11 December 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1307.60072
MathSciNet: MR3296526
Digital Object Identifier: 10.1214/EJP.v19-3175

Subjects:
Primary: 60H07
Secondary: 60H30

JOURNAL ARTICLE
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Vol.19 • 2014
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