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

Barrieu, Pauline and Schoutens, Wim (2006) Iterates of the infinitesimal generator and space-time harmonic polynomials of a Markov process. Journal of Computational and Applied Mathematics, 186 (1). pp. 300-323. ISSN 0377-0427

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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.

Item Type: Article
Official URL: http://www.sciencedirect.com/science/journal/03770...
Additional Information: © 2007 Elsevier B.V. All rights reserved
Library of Congress subject classification: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Sets: Departments > Statistics
Research centres and groups > Centre for the Analysis of Time Series (CATS)
Research centres and groups > Risk and Stochastics Group
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 01 Nov 2007
URL: http://eprints.lse.ac.uk/2832/

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