Reciprocal class of jump processes
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 pro...
| Main Authors: | , , |
|---|---|
| Format: | Others |
| Language: | English |
| Published: |
Universität Potsdam
2014
|
| Subjects: | |
| Online Access: | http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-70776 http://opus.kobv.de/ubp/volltexte/2014/7077/ |
| Summary: | 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. |
|---|