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On the distances between probability density functions


 
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1. Title Title of document On the distances between probability density functions
 
2. Creator Author's name, affiliation, country Vlad Bally; Université Paris-Est Marne-la-Vallée; France
 
2. Creator Author's name, affiliation, country Lucia Caramellino; Università di Roma Tor Vergata; Italy
 
3. Subject Discipline(s)
 
3. Subject Keyword(s)
 
3. Subject Subject classification 60H07, 60H30
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2014-12-11
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3175
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3175
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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