A Class of Piecewise Deterministic Markov Processes

G. Colombo, P. Dai Pra

2001, v.7, №2, 251-287

ABSTRACT

A class of not necessarily homogeneous Markov processes is constructed. These processes are characterized by a property of loss of memory after they leave the trajectory of a given deterministic flow. With this property, the law of the process is completely determined by the marginal distributions. The regularity of sample paths is also analyzed in detail. As an example, magnitude-frequency models for earthquakes are discussed.

Keywords: jump processes,order relations between probability measures

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