Gaussian lower bounds for the density via Malliavin calculus
type: Item
instance of: scholarly article
title: Gaussian lower bounds for the density via Malliavin calculus
zbMATH Open document ID: 1478.60169
author: Tien Dung Nguyen
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2020-08-03T00:00:00Z
review text: Representations as expectation and lower bounds are derived for the probability density of a Wiener functional \(F\) using a classical integration by parts formula in the Malliavin calculus. In comparison with other approaches, those bounds only require a one-sided inequality on the term \(\langle DF,-DL^{-1}F\rangle_{L^2(\mathbb{R}_+)}\), where \(DF\) and \(L\), respectively, denote the Malliavin gradient of the functional \(F\) and the Ornstein-Uhlenbeck operator. Applications are given to additive functionals of Gaussian processes and to stochastic differential equations with fractional Brownian noise.
reviewed by: Nicolas Privault
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G22
zbMATH DE Number: 7226761
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: lower bounds
zbMATH Keywords: probability densities
zbMATH Keywords: fractional Brownian motion
MaRDI profile type: Publication
full work available at URL: crmath.13
OpenAlex ID: W3013578968
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DOI: 10.5802/CRMATH.13
description: scientific article; zbMATH DE number 7226761