Header menu link for other important links
X
Markov processes, time-space harmonic functions and polynomials
Published in ELSEVIER SCIENCE BV
2008
Volume: 78
   
Issue: 18
Pages: 3277 - 3280
Abstract
We consider stochastic processes (Mt)t ≥ 0 for which the class V 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 Vt {colon equals} {f (t, {dot operator})} {divides} f ∈ V} in Lp (μt) for any p ≥ 1, where μt 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. © 2008 Elsevier B.V. All rights reserved.
About the journal
JournalData powered by TypesetStatistics and Probability Letters
PublisherData powered by TypesetELSEVIER SCIENCE BV
ISSN0167-7152
Open AccessNo