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

By Pauline Barrieu and Wim Schoutens

Abstract

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

Topics: HA Statistics, QA Mathematics
Year: 2006
DOI identifier: 10.1016/j.cam.2005.04.014
OAI identifier: oai:eprints.lse.ac.uk:2832
Provided by: LSE Research Online
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