Recession of some relativistic Markov processes

Some Peculiar Semi-markov Processes

Optimal Stopping Problems for Some Markov Processes

In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller processes. This generalizes the result of Beibel and Lerche [Statist. Sinica 7 (1997) 93–108] and [Teor. Veroyatn. Primen. 45 (2000) 657–669] and Irles and Pa...

Some simple but challenging Markov processes

In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . . ) and they are mathematically rich. Their mathematical study relies on coupling method, spectral decomposition, PDE technics, functional inequalities. We also relate these sim...

ON THE INFINITE ORDER MARKOV PROCESSES

The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.

On the Lengths of Excursions of Some Markov Processes

Results are obtained regarding the distribution of the ranked lengths of component intervals in the complement of the random set of times when a recurrent Markov process returns to its starting point. Various martingales are described in terms of the L evy measure of the Poisson point process of interval lengths on the local time scale. The martingales derived from the zero set of a one-dimensi...