Lp estimates for Feynman-Kac propagators with time-dependent reference measures

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:365

Article

Eberle, Andreas¹  Marinelli, Carlo¹ 

[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

关键词: Time-inhomogeneous Markov processes;    Feynman-Kac formula;    Dirichlet forms;    Poincare inequalities;    Logarithmic Sobolev inequalities;    Markov semigroups;    L-p estimates;    Markov Chain Monte Carlo;    Sequential Monte Carlo;    Importance sampling;   

DOI  :  10.1016/j.jmaa.2009.10.019

来源: Elsevier

【 摘 要 】

We introduce a class of time-inhomogeneous transition operators of Feynman-Kac type that can be considered as a generalization of symmetric Markov semigroups to the case of a time-dependent reference measure. Applying weighted Poincare and logarithmic Sobolev inequalities, we derive L-p -> L-p and L-p -> L-q estimates for the transition operators. Since the operators are not Markovian, the estimates depend crucially on the value of p. Our studies are motivated by applications to sequential Markov Chain Monte Carlo methods. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free