Averaging for some simple constrained Markov processes

• Autorzy: Genadot Alexandre

Identyfikatory

DOI

10.19195/0208-4147.39.1.10

• Języki publikacji: EN

Abstrakty

EN

In this paper, a class of piecewise deterministic Markov processes with underlying fast dynamic is studied. By using a “penalty method”, an averaging result is obtained when the underlying dynamic is infinitely accelerated. The features of the averaged process, which is still a piecewise deterministic Markov process, are fully described.

Słowa kluczowe

EN

piecewise deterministic Markov process; averaging; constrained Markov process

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 1
• Strony: 139--158
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Genadot Alexandre

• Institut de Mathématiques de Bordeaux and INRIA Bordeaux-Sud-Ouest, Team CQFD, Institut de Mathématiques de Bordeaux UMR 5251, Université de Bordeaux, 351, Cours de la Libération, F 33 405 Talence, France

Bibliografia

• [1] P. Billingsley, Convergence of Probability Measures, Wiley, 2013.
• [2] A. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biol. Cybernet. 95 (1) (2006), pp. 1-19.
• [3] C. Costantini and T. G. Kurtz, Viscosity methods giving uniqueness for martingale problems, Electron. J. Probab. 20 (2015), pp. 1-27.
• [4] M. H. A. Davis, Markov Models and Optimization, Chapman and Hall, 1993.
• [5] S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence,Wiley, 2009.
• [6] T. G. Kurtz, Martingale problems for constrained Markov processes, in: Recent Advances in Stochastic Calculus, J. S. Baras and V. Mirelli (Eds.), Springer, New York 1990.
• [7] T. G. Kurtz, Random time changes and convergence in distribution under the Meyer-Zheng conditions, Ann. Probab. 19 (3) (1991), pp. 1010-1034.
• [8] T. G. Kurtz, Averaging for martingale problems and stochastic approximation, in: Applied Stochastic Analysis, I. Karatzas and D. Ocone (Eds.), Springer, 1992, pp. 186-209.
• [9] G. A. Pavliotis and A. M. Stuart, Multiscale Methods: Averaging and Homogenization, Springer, Berlin 2008.
• [10] G. Yin and Q. Zhang, Discrete-Time Markov Chains: Two-Time-Scale Methods and Applications, Springer, New York 2006.