Stochastic flows acting on Schwartz distributions
type: Item
instance of: scholarly article
title: Stochastic flows acting on Schwartz distributions
zbMATH Open document ID: 0818.60044
DOI: 10.1007/BF02214270
author: Hiroshi Kunita
published in: Journal of Theoretical Probability
publication date: 1995-08-13T00:00:00Z
review text: Consider a Schwartz distribution \(T\) and the stochastic flow \(\varphi_{s,t}\) generated by a stochastic differential equation; the composition of \(T\) with \(\varphi\) is defined as a random distribution; the spatial regularity of this variable is studied in terms of Sobolev spaces. For the time regularity, after defining a stochastic integral, a generalized Itô's formula is proved when \(T = T(t)\) is a semimartingale. These results are applied to the regularity of semigroups, and to the existence and spatial regularity of a local time for a one-dimensional flow. Moreover, the relation with the pull-back defined by Watanabe is discussed.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 566134
zbMATH Keywords: stochastic flow
zbMATH Keywords: Schwartz distributions
zbMATH Keywords: generalized Itô's formula
zbMATH Keywords: local time
reviewed by: Jean Picard
MaRDI profile type: Publication
cites work: Hypoelliptic second order differential equations
cites work: Q3992729
cites work: Stochastic Integrals Based on Martingales Taking Values in Hilbert Space
cites work: Q3995203
cites work: Q3684932
cites work: Q3996259
full work available at URL: https://doi.org/10.1007/bf02214270
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description: scientific article; zbMATH DE number 566134