Some simple but challenging Markov processes

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...

Some Peculiar Semi-markov Processes

A Simple, but Challenging, Model of Computational Design Creativity Evaluation

This paper presents a simple model of computational design creativity evaluation, presenting its components with rationale. Components are linked to recent research. The model assumes that the product, not the process, is being evaluated, and that evaluation is done by comparison with descriptions of existing products using a set of aspects that each suggest creativity. Not every evaluation wil...

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...

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.