Iterates of the infinitesimal generator and space–time harmonic polynomials of a Markov process
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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.
论文关键词:Markov process,Lévy processes,Subordinators,Space–time harmonic polynomials,Martingales,Infinitesimal generator,Stirling numbers
论文评审过程:Received 28 September 2004, Revised 23 March 2005, Available online 4 June 2005.
论文官网地址:https://doi.org/10.1016/j.cam.2005.04.014