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Reciprocal class of random walks on an Abelian group

  • Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of a continuous time random walk with values in a countable Abelian group, we compute explicitly its reciprocal characteristics and we present an integral characterization of it. Our main tool is a new iterated version of the celebrated Mecke's formula from the point process theory, which allows us to study, as transformation on the path space, the addition of random loops. Thanks to the lattice structure of the set of loops, we even obtain a sharp characterization. At the end, we discuss several examples to illustrate the richness of reciprocal classes. We observe how their structure depends on the algebraic properties of the underlying group.

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Metadaten
Author details:Giovanni ConfortiGND, Sylvie RoellyGND
URN:urn:nbn:de:kobv:517-opus-72604
ISSN:2193-6943
Publication series (Volume number):Preprints des Instituts für Mathematik der Universität Potsdam (4 (2015) 1)
Publisher:Universitätsverlag Potsdam
Place of publishing:Potsdam
Publication type:Preprint
Language:English
Year of first publication:2015
Publication year:2015
Publishing institution:Universität Potsdam
Publishing institution:Universitätsverlag Potsdam
Release date:2015/01/07
Tag:random walk on Abelian group; reciprocal class; stochastic bridge
Volume:4
Issue:1
Number of pages:22
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Bxx Probability theory on algebraic and topological structures / 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J25 Continuous-time Markov processes on general state spaces
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J28 Applications of continuous-time Markov processes on discrete state spaces
Collection(s):Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2015
Publishing method:Universitätsverlag Potsdam
License (German):License LogoKeine öffentliche Lizenz: Unter Urheberrechtsschutz
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