Bornes quantitatives pour la convergence en temps long de processus de Markov

National audienceSi l'on sait assez bien décrire qualitativement le comportement de nombreux processus de Markov (existence et unicité d'une mesure invariante, convergence exponentielle à l'équilibre, etc), il est en général beaucoup plus difficile d'obtenir des bornes explicites pour la vitesse de convergence à l'équilibre

Allocation conjointe de puissance et rendement d'un utilisateur cognitif exploitant les retransmissions d'un utilisateur primaire : le cas du canal en Z

National audienceDans cet article, nous considérons le problème de l’allocation conjointe de puissance et de rendement pour un utilisateur secondaire exploitant le protocole de retransmission d’un utilisateur primaire. Nous proposons un algorithme, basé sur les Processus de Markov Décisionnels (MDP), permettant de calculer une allocation optimale pour le problème de la maximisation du débit de l’utilisateur secondaire tout en garantissant un débit minimal pour l’utilisateur primaire

Hitting Times in Markov Chains with Restart and their Application to Network Centrality

Motivated by applications in telecommunications, computer scienceand physics, we consider a discrete-time Markov process withrestart. At each step the process eitherwith a positive probability restarts from a given distribution, orwith the complementary probability continues according to a Markovtransition kernel. The main contribution of the present work is thatwe obtain an explicit expression for the expectation of the hittingtime (to a given target set) of the process with restart.The formula is convenient when considering the problem of optimizationof the expected hitting time with respect to the restart probability.We illustrate our results with two examplesin uncountable and countable state spaces andwith an application to network centrality

Absolutely Continuous Compensators

We give sufficient conditions on the underlying filtration such that all totally inaccessible stopping times have compensators which are absolutely continuous. If a semimartingale, strong Markov process X has a representation as a solution of a stochastic differential equation driven by a Wiener process, Lebesgue measure, and a Poisson random measure, then all compensators of totally inaccessible stopping times are absolutely continuous with respect to the minimal filtration generated by X. However Cinlar and Jacod have shown that all semimartingale strong Markov processes, up to a change of time and space, have such a representation

Arr\^et optimal pour les processus de Markov forts et les fonctions affines

In this Note we study optimal stopping problems for strong Markov processes and affine functions. We give a justification of the Snell envelope form using standard results of optimal stopping. We also justify the convexity of the value function, and without a priori restriction to a particular class of stopping times, we deduce that the smallest optimal stopping time is necessarily a hitting time