Bernoulli

  • Bernoulli
  • Volume 23, Number 3 (2017), 1518-1537.

Bridge mixtures of random walks on an Abelian group

Giovanni Conforti and Sylvie Roelly

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Abstract

In this paper, we characterize (mixtures of) bridges of a continuous time random walk with values in a countable Abelian group. Our main tool is a conditional version of 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 such random processes. We observe in particular how their structure depends on the algebraic properties of the underlying group.

Article information

Source
Bernoulli, Volume 23, Number 3 (2017), 1518-1537.

Dates
Received: January 2015
Revised: September 2015
First available in Project Euclid: 17 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1489737616

Digital Object Identifier
doi:10.3150/15-BEJ783

Mathematical Reviews number (MathSciNet)
MR3624869

Zentralblatt MATH identifier
06714310

Keywords
random walk on Abelian group reciprocal class stochastic bridge

Citation

Conforti, Giovanni; Roelly, Sylvie. Bridge mixtures of random walks on an Abelian group. Bernoulli 23 (2017), no. 3, 1518--1537. doi:10.3150/15-BEJ783. https://projecteuclid.org/euclid.bj/1489737616


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