Invariant measure for the stochastic Cauchy problem driven by a cylindrical Levy process

被引：1

作者：

Kumar, Umesh ^{[1
]}

Riedle, Markus ^{[2
,3
]}

机构：

[1] Univ Delhi, Rajdhani Coll, Dept Math, New Delhi 110015, India

[2] Kings Coll London, Dept Math, London WC2R 2LS, England

[3] Tech Univ Dresden, Inst Math Stochast, Fac Math, D-01062 Dresden, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 493卷 / 02期

关键词：

Cylindrical Levy processes; Cauchy problem; Invariant measures; Stationary distributions; Mehler semigroup; GENERALIZED MEHLER SEMIGROUPS;

D O I：

10.1016/j.jmaa.2020.124536

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we present sufficient conditions for the existence of a stationary solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical Levy process, and show that these conditions are also necessary if the semigroup is stable, in which case the invariant measure is unique. For typical situations such as the heat equation, we significantly simplify these conditions without assuming any further restrictions on the driving cylindrical Levy process and demonstrate their application in some examples. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：26

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