TY  - INPR
A1  - Conforti, Giovanni
A1  - Roelly, Sylvie
T1  - Reciprocal class of random walks on an Abelian group
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 1 
KW  - reciprocal class
KW  - stochastic bridge
KW  - random walk on Abelian group
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-72604
SN  - 2193-6943
VL  - 4
IS  - 1
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Conforti, Giovanni
A1  - Léonard, Christian
A1  - Murr, Rüdiger
A1  - Roelly, Sylvie
T1  - Bridges of Markov counting processes : reciprocal classes and duality formulas
N2  - Processes having the same bridges are said to belong to the same reciprocal class. In this article we analyze reciprocal classes of Markov counting processes by identifying their reciprocal invariants and we characterize them as the set of counting processes satisfying some duality formula.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 9 
KW  - counting process
KW  - bridge
KW  - reciprocal class
KW  - duality formula
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-71855
SN  - 2193-6943
VL  - 3
IS  - 9
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  -