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

Authors:
Pauline Barrieu;Wim Schoutens
Affiliations:
London School of Economics, Statistics Department, Houghton Street, London WC2A 2AE, UK;K.U. Leuven, U.C.S., W. De Croylaan 54, 3001 Leuven, Belgium
Venue:
Journal of Computational and Applied Mathematics - Special issue: Jef Teugels
Year:
2006

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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.