Delay differential equations driven by Levy processes: Stationarity and Feller properties

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:116

Article

Reiss, M. ; Riedle, M. ; van Gaans, O.

关键词: Feller process;    invariant measure;    Levy process;    semimartingale characteristic;    stationary solution;    stochastic equation with delay;    stochastic functional differential equation;   

DOI  :  10.1016/j.spa.2006.03.002

来源: Elsevier

【 摘 要 】

We consider a stochastic delay differential equation driven by a general Levy process. Both the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment process is eventually Feller, but in general not eventually strong Feller on the Skorokhod space. The existence of an invariant measure is shown by proving tightness of the segments using semimartingale characteristics and the Krylov-Bogoliubov method. A counterexample shows that the stationary solution in completely general situations may not be unique, but in more specific cases uniqueness is established. (C) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

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