Reciprocal classes of random walks on graphs

The reciprocal class of a Markov path measure is the set of all mixtures of its bridges. We give characterizations of the reciprocal class of a continuous-time Markov random walk on a graph. Our main result is in terms of some reciprocal characteristics whose expression only depends on the jump inte...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 27; no. 6; pp. 1870 - 1896
Main Authors Conforti, Giovanni, Léonard, Christian
Format Journal Article
LanguageEnglish
Published Elsevier 2017
Subjects
Mathematics
Probability
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ISSN0304-4149
1879-209X

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Summary:The reciprocal class of a Markov path measure is the set of all mixtures of its bridges. We give characterizations of the reciprocal class of a continuous-time Markov random walk on a graph. Our main result is in terms of some reciprocal characteristics whose expression only depends on the jump intensity. We also characterize the reciprocal class by means of Taylor expansions in small time of some conditional probabilities. Our measure-theoretical approach allows to extend significantly already known results on the subject. The abstract results are illustrated by several examples.
ISSN:0304-4149
1879-209X