Skip to Main content Skip to Navigation
Journal articles

Convergence and regularity of probability laws by using an interpolation method

Vlad Bally 1, 2 Lucia Caramellino 3
2 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
Abstract : Fournier and Printems [Bernoulli, 2010] 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, 2014] 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [35 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01109276
Contributor : Lucia Caramellino <>
Submitted on : Monday, January 8, 2018 - 12:17:30 PM
Last modification on : Monday, May 31, 2021 - 11:14:15 PM
Long-term archiving on: : Wednesday, May 23, 2018 - 3:04:53 PM

File

Last-version-for-AP.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01109276, version 2

Citation

Vlad Bally, Lucia Caramellino. Convergence and regularity of probability laws by using an interpolation method. Annals of Probability, Institute of Mathematical Statistics, 2017, 45 (2). ⟨hal-01109276v2⟩

Share

Metrics

Record views

494

Files downloads

1086