Markov processes, time-space harmonic functions and polynomials

Arindam Sengupta

Statistics & Probability Letters, 2008, vol. 78, issue 18, 3277-3280

Abstract: We consider stochastic processes (Mt)t>=0 for which the class of time-space harmonic functions is rich enough to yield the Markov property for the process. In particular, we prove that denseness for all t>=0 of in Lp([mu]t) for any p>=1, where [mu]t denotes the law of Mt, is sufficient to guarantee the Markov property. We use this to improve upon a result of [Sengupta, Arindam, 2000. Time-space harmonic polynomials martingales for continuous-time processes and an extension. Journal of Theoretical Probability 13 (4), 951-976] concerning p-harmonizability, describe two new methods for constructing time-space harmonic polynomials and apply them to get some interesting examples.

Date: 2008
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