Regular Article: A Unified Approach to Generalized Stirling Numbers
Advances in Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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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.