Journal of computational and applied mathematics vol:186 issue:1 pages:300-323
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.