@article{EJP3175,
author = {Vlad Bally and Lucia Caramellino},
title = {On the distances between probability density functions},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {},
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.},
pages = {no. 110, 1-33},
issn = {1083-6489},
doi = {10.1214/EJP.v19-3175},
url = {http://ejp.ejpecp.org/article/view/3175}}