TY  - JOUR
A1  - Conforti, Giovanni
A1  - Pra, Paolo Dai
A1  - Roelly, Sylvie
T1  - Reciprocal Class of Jump Processes
JF  - Journal of theoretical probability
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 . 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 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.
KW  - Reciprocal processes
KW  - Stochastic bridges
KW  - Jump processes
KW  - Compound Poisson processes
Y1  - 2015
U6  - https://doi.org/10.1007/s10959-015-0655-3
SN  - 0894-9840
SN  - 1572-9230
VL  - 30
SP  - 551
EP  - 580
PB  - Springer
CY  - New York
ER  -