Malliavin calculus on the Wiener-Poisson space and its application to canonical SDE with jumps
type: Item
instance of: scholarly article
title: Malliavin calculus on the Wiener-Poisson space and its application to canonical SDE with jumps
zbMATH Open document ID: 1107.60028
author: Yasushi Ishikawa
author: Hiroshi Kunita
published in: Stochastic Processes and their Applications
publication date: 2007-01-09T00:00:00Z
review text: Consider a so-called canonical stochastic differential equation driven by a multidimensional Lévy process \(Z\). The aim is to find conditions under which the solution has a \(C^\infty\) density. Classical Malliavin's calculus is devoted to the case where \(Z\) is a Wiener process; some other works are devoted to the case where \(Z\) is a pure jump Lévy process. Here, the two cases are mixed. The authors assume a non-degeneracy condition on the coefficients of the equations, and on the matrix \(A+B\) where \(A\) is the covariance matrix of the Brownian part of \(Z\), and \(B\) is a matrix related to the Lévy measure of \(Z\) (more precisely to the small jumps of \(Z\)). Under these conditions, the existence of a smooth density is proved.
reviewed by: Jean Picard
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 5083377
zbMATH Keywords: jump processes
zbMATH Keywords: canonical stochastic differential equation
zbMATH Keywords: smooth density
MaRDI profile type: Publication
full work available at URL: j.spa.2006.04.013
OpenAlex ID: W2038336958
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DOI: 10.1016/J.SPA.2006.04.013
description: scientific article; zbMATH DE number 5083377