TY  - INPR
A1  - Conforti, Giovanni
A1  - Dai Pra, Paolo
A1  - Roelly, Sylvie
T1  - Reciprocal class of jump processes
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 compound Poisson processes whose jumps belong to a finite set A in R^d. We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of A plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 6 
KW  - reciprocal processes
KW  - stochastic bridges
KW  - jump processes
KW  - compound Poisson processes
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70776
SN  - 2193-6943
VL  - 3
IS  - 6
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Léonard, Christian
A1  - Roelly, Sylvie
A1  - Zambrini, Jean-Claude
T1  - Temporal symmetry of some classes of stochastic processes
N2  - In this article we analyse the structure of Markov processes and reciprocal processes to underline their time symmetrical properties, and to compare them. Our originality consists in adopting a unifying approach of reciprocal processes, independently of special frameworks in which the theory was developped till now (diffusions, or pure jump processes). This leads to some new results, too.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2 (2013) 7 
KW  - Markov processes
KW  - reciprocal processes
KW  - time symmetry
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-64599
SN  - 2193-6943
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  -