On analyticity of Ornstein-Uhlenbeck semigroups
type: Item
instance of: scholarly article
title: On analyticity of Ornstein-Uhlenbeck semigroups
zbMATH Open document ID: 1026.47506
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2002-10-31T00:00:00Z
review text: Summary: Let \((R_t)\) be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let \(\mu\) denote its Gaussian invariant measure. We show that the semigroup \((R_t)\) is analytic in \(L^2(\mu)\) if and only if its generator is variational. In particular, we show that the transition semigroup of a finite-dimensional Ornstein-Uhlenbeck process is analytic if and only if the Wiener process is nondegenerate.
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 1822108
zbMATH Keywords: Ornstein-Uhlenbeck semigroup
zbMATH Keywords: bilinear form
zbMATH Keywords: variational generator
zbMATH Keywords: polynomial chaos
zbMATH Keywords: second quantization
author: B. Goldys
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1822108