TY  - JOUR
A1  - Conforti, Giovanni
A1  - Roelly, Sylvie
T1  - Bridge mixtures of random walks on an Abelian group
JF  - Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability
KW  - random walk on Abelian group
KW  - reciprocal class
KW  - stochastic bridge
Y1  - 2017
U6  - https://doi.org/10.3150/15-BEJ783
SN  - 1350-7265
SN  - 1573-9759
VL  - 23
SP  - 1518
EP  - 1537
PB  - International Statistical Institute
CY  - Voorburg
ER  - 
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  - GEN
A1  - Roelly, Sylvie
A1  - Thieullen, Michèle
T1  - Duality formula for the bridges of a Brownian diffusion : application to gradient drifts
N2  - In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths C[0; 1]; R-d) Our techniques provide a characterization of gradient diffusions by a duality formula and, in case of reversibility, a generalization of a result of Kolmogorov.
KW  - reciprocal processes
KW  - stochastic bridge
KW  - mixture of bridges
KW  - integration by parts formula
KW  - Malliavin calculus
KW  - entropy
KW  - time reversal
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6710
ER  -