Iterates of the infinitesimal generator and space-time harmonic polynomials of a Markov process

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:186

Article

Barrieu, P ; Schoutens, W

关键词: Markov process;    Levy processes;    subordinators;    space-time harmonic polynomials;    martingales;    infinitesimal generator;    Stirling numbers;   

DOI  :  10.1016/j.cam.2005.04.014

来源: Elsevier

【 摘 要 】

We relate iterates of the infinitesimal generator of a Markov process to space-time harmonic functions. First, we develop the theory for a general Markov process and create a family a space-time martingales. Next, we investigate the special class of subordinators. Combinatorics results on space-time harmonic polynomials and generalized Stirling numbers are developed and interpreted from a probabilistic point of view. Finally, we introduce the notion of pairs of subordinators in duality, investigate the implications on the associated martingales and consider some explicit examples. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

Free