. Bouton, C. Pagès-]-bouton, and G. Pagès, About the multidimensional competitive learning vector quantization algorithm with constant gain, The Annals of Applied Probability, vol.7, issue.3, 1997.
DOI : 10.1214/aoap/1034801249

. Brandejsky, Numerical Methods for the Exit Time of a Piecewise-Deterministic Markov Process, Advances in Applied Probability, vol.44, issue.01, pp.196-225, 2012.
DOI : 10.1016/j.spl.2007.12.016
URL : https://hal.archives-ouvertes.fr/hal-00546339

. Chiquet, . Limnios, J. Chiquet, and N. Limnios, A method to compute the transition function of a piecewise deterministic Markov process with application to reliability, Statistics & Probability Letters, vol.78, issue.12, pp.781397-1403, 2008.
DOI : 10.1016/j.spl.2007.12.016
URL : https://hal.archives-ouvertes.fr/hal-00260732

M. H. Davis, Markov models and optimization, of Monographs on Statistics and Applied Probability, 1993.
DOI : 10.1007/978-1-4899-4483-2

. De-saporta, Numerical method for optimal stopping of piecewise deterministic Markov processes, The Annals of Applied Probability, vol.20, issue.5, pp.1607-1637, 2010.
DOI : 10.1214/09-AAP667
URL : https://hal.archives-ouvertes.fr/hal-00367964

W. Feller, An introduction to probability theory and its applications, 1966.

. Helmes, Computing Moments of the Exit Time Distribution for Markov Processes by Linear Programming, Operations Research, vol.49, issue.4, pp.516-530, 2001.
DOI : 10.1287/opre.49.4.516.11221

. Kurtz, . Stockbridge, T. G. Kurtz, and R. H. Stockbridge, Existence of Markov Controls and Characterization of Optimal Markov Controls, SIAM Journal on Control and Optimization, vol.36, issue.2, pp.609-653, 1998.
DOI : 10.1137/S0363012995295516

J. B. Lasserre, SDP versus LP relaxations for polynomial programming, Novel approaches to hard discrete optimization, pp.143-154, 2001.
DOI : 10.1090/fic/037/09

S. Vs, LP relaxations for the moment approach in some performance evaluation problems, Stoch. Models, vol.20, issue.4, pp.439-456

2. 9. Schéma-d-'approximation, . Et, and . Bibliographiearjas, Filtering the histories of a partially observed marked point process, Stochastic Process. Appl, vol.40, issue.2, pp.225-250, 1992.

P. Brémaud, Point processes and queues, 1981.
DOI : 10.1007/978-1-4684-9477-8

M. H. Davis, Markov models and optimization, of Monographs on Statistics and Applied Probability, 1993.
DOI : 10.1007/978-1-4899-4483-2

U. S. Gugerli, Optimal stopping of a piecewise-deterministic markov process, Stochastics, vol.440, issue.4, pp.221-236, 1986.
DOI : 10.1090/S0002-9947-1952-0050209-9

. Kalman, . Bucy, R. E. Kalman, and R. S. Bucy, New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, vol.83, issue.1, pp.95-108, 1961.
DOI : 10.1115/1.3658902

M. Ludkovski, A simulation approach to optimal stopping under partial information. Stochastic Process, Appl, vol.119, issue.12, pp.4061-4087, 2009.

J. Ouvrard, Probabilités 2, 2004.

. Pham, Approximation by quantization of the filter process and applications to optimal stopping problems under partial observation, Monte Carlo Methods and Applications, vol.11, issue.1, pp.57-81, 2005.
DOI : 10.1515/1569396054027283
URL : https://hal.archives-ouvertes.fr/hal-00101833

.. De-poisson, Résultats des simulations pour la distribution du temps de sortie pour le processus, p.143

. Bibliographie and . Arjas, Filtering the histories of a partially observed marked point process, Stochastic Process. Appl, vol.40, issue.2, pp.225-250, 1992.

V. Bally and G. Pagès, A quantization algorithm for solving multidimensional discrete-time optimal stopping problems, Bernoulli, vol.9, issue.6, pp.1003-1049, 2003.
DOI : 10.3150/bj/1072215199
URL : https://hal.archives-ouvertes.fr/hal-00104798

. Bally, A QUANTIZATION TREE METHOD FOR PRICING AND HEDGING MULTIDIMENSIONAL AMERICAN OPTIONS, Mathematical Finance, vol.26, issue.2, pp.119-168, 2005.
DOI : 10.1287/moor.27.1.121.341
URL : https://hal.archives-ouvertes.fr/inria-00072123

. Brandejsky, Numerical method for expectations of piecewise deterministic Markov processes, Communications in Applied Mathematics and Computational Science, vol.7, issue.1, pp.63-104, 2012.
DOI : 10.2140/camcos.2012.7.63

P. Brémaud, Point processes and queues, 1981.
DOI : 10.1007/978-1-4684-9477-8

. Busic, Perfect Sampling of Markov Chains with Piecewise Homogeneous Events. Performance Evaluation A method to compute the transition function of a piecewise deterministic Markov process with application to reliability, Statist. Probab. Lett, issue.12, pp.781397-1403, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00787997

. Chiquet, Piecewise deterministic Markov processes applied to fatigue crack growth modelling, Journal of Statistical Planning and Inference, vol.139, issue.5, pp.1391657-1667, 2009.
DOI : 10.1016/j.jspi.2008.05.034

J. Çinlar, E. Çinlar, and J. Jacod, Representation of semimartingale Markov processes in terms of Wiener processes and Poisson random measures, Seminar on Stochastic Processes, pp.159-242, 1981.

. Cocozza-thivent, A finite-volume scheme for dynamic reliability models, IMA Journal of Numerical Analysis, vol.26, issue.3, pp.446-471, 2006.
DOI : 10.1093/imanum/drl001
URL : https://hal.archives-ouvertes.fr/hal-00693102

O. L. Costa, Impulse control of piecewise-deterministic processes via linear programming, IEEE Transactions on Automatic Control, vol.36, issue.3, pp.371-375, 1991.
DOI : 10.1109/9.73574

C. , D. Costa, O. L. Davis, and M. H. , Impulse control of piecewise-deterministic processes, Math. Control Signals Systems, vol.2, issue.3, pp.187-206, 1989.

C. , D. Costa, O. L. Dufour, and F. , Stability and ergodicity of piecewise deterministic Markov processes, SIAM J. Control Optim, vol.47, issue.2, pp.1053-1077, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00268162

E. Dassios, A. Dassios, and P. Embrechts, Martingales and insurance risk, Communications in Statistics. Stochastic Models, vol.58, issue.46, pp.181-217, 1989.
DOI : 10.1287/moor.3.1.57

M. H. Davis, Piecewise-deterministic Markov processes, J. Roy. Statist. Soc. Ser. B, vol.46, issue.3, pp.353-388, 1984.
DOI : 10.1007/978-1-4899-4483-2_2

M. H. Davis, Markov models and optimization, of Monographs on Statistics and Applied Probability, 1993.
DOI : 10.1007/978-1-4899-4483-2

. Davis, Optimal capacity expansion under uncertainty, Advances in Applied Probability, vol.13, issue.01, pp.156-176, 1987.
DOI : 10.1016/0309-1708(77)90006-9

. De-saporta, B. Dufour-de-saporta, and F. Dufour, Numerical method for impulse control of piecewise deterministic Markov processes, Automatica, vol.48, issue.5, 2011.
DOI : 10.1016/j.automatica.2012.02.031
URL : https://hal.archives-ouvertes.fr/hal-00541413

M. A. Dempster, Optimal control of piecewise deterministic Markov processes, Applied stochastic analysis, pp.303-325, 1989.

Y. Dempster, M. A. Dempster, and J. J. Ye, Impulse Control of Piecewise Deterministic Markov Processes, The Annals of Applied Probability, vol.5, issue.2, pp.399-423, 1995.
DOI : 10.1214/aoap/1177004771

C. Dufour, F. Dufour, and O. L. Costa, Stability of Piecewise-Deterministic Markov Processes, SIAM Journal on Control and Optimization, vol.37, issue.5, pp.1483-1502, 1999.
DOI : 10.1137/S0363012997330890
URL : https://hal.archives-ouvertes.fr/hal-00268162

P. Embrechts and H. Schmidli, Ruin estimation for a general insurance risk model, Advances in Applied Probability, vol.46, issue.02, pp.404-422, 1994.
DOI : 10.1080/15326348908807105

B. Everdij, M. H. Everdij, and H. A. Blom, Piecewise deterministic Markov processes represented by dynamically coloured Petri nets, Stochastics An International Journal of Probability and Stochastic Processes, vol.691, issue.1, pp.1-29, 2005.
DOI : 10.1109/9.665073

. Eymard, An implicit finite volume scheme for a scalar hyperbolic problem with measure data related to piecewise deterministic Markov processes, Journal of Computational and Applied Mathematics, vol.222, issue.2, pp.293-323, 2008.
DOI : 10.1016/j.cam.2007.10.053
URL : https://hal.archives-ouvertes.fr/hal-00693134

. Faggionato, Averaging and large deviation principles for fully-coupled piecewise deterministic Markov processes and applications to molecular motors. Markov Process, pp.497-548, 2010.

. Faggionato, Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes, Journal of Statistical Physics, vol.45, issue.1/2, pp.259-304, 2009.
DOI : 10.1007/s10955-009-9850-x

W. Feller, An introduction to probability theory and its applications, 1966.

K. Gonzalez, Contribution à l'étude des processus markoviens déterministes par morceaux, 2010.

R. Graham, C. Graham, and P. Robert, Interacting multi-class transmissions in large stochastic networks, The Annals of Applied Probability, vol.19, issue.6, pp.2334-2361, 2009.
DOI : 10.1214/09-AAP614
URL : https://hal.archives-ouvertes.fr/inria-00326156

R. Graham, C. Graham, and P. Robert, A Multi-Class Mean-Field Model with Graph Structure for TCP Flows, Progress in industrial mathematics at ECMI 2008, pp.125-131, 2010.
DOI : 10.1007/978-3-642-12110-4_13

. Gray, . Neuhoff, R. M. Gray, and D. L. Neuhoff, Quantization, IEEE Transactions on Information Theory, vol.44, issue.6, pp.2325-2383, 1998.
DOI : 10.1109/18.720541

U. S. Gugerli, Optimal stopping of a piecewise-deterministic markov process, Stochastics, vol.440, issue.4, pp.221-236, 1986.
DOI : 10.1090/S0002-9947-1952-0050209-9

. Helmes, Computing Moments of the Exit Time Distribution for Markov Processes by Linear Programming, Operations Research, vol.49, issue.4, pp.516-530, 2001.
DOI : 10.1287/opre.49.4.516.11221

M. Jacobsen, Point process theory and applications. Probability and its Applications, Birkhäuser Boston Inc, 2006.

. Kalman, . Bucy, R. E. Kalman, and R. S. Bucy, New Results in Linear Filtering and Prediction Theory, Journal of Basic Engineering, vol.83, issue.1, pp.95-108, 1961.
DOI : 10.1115/1.3658902

. Koroliuk, . Limnios, V. S. Koroliuk, and N. Limnios, Stochastic systems in merging phase space, 2005.
DOI : 10.1142/5979

J. B. Lasserre, SDP versus LP relaxations for polynomial programming, Novel approaches to hard discrete optimization, pp.143-154, 2001.
DOI : 10.1090/fic/037/09

S. Vs, LP relaxations for the moment approach in some performance evaluation problems, Stoch. Models, vol.20, issue.4, pp.439-456

S. M. Lenhart, Viscosity solutions associated with impulse control problems for piecewise-deterministic processes, International Journal of Mathematics and Mathematical Sciences, vol.12, issue.1, pp.145-157, 1989.
DOI : 10.1155/S0161171289000207

M. Ludkovski, A simulation approach to optimal stopping under partial information. Stochastic Process, Appl, vol.119, issue.12, pp.4061-4087, 2009.

J. Ouvrard, Probabilités 2, 2004.

G. Pagès, A space quantization method for numerical integration, Journal of Computational and Applied Mathematics, vol.89, issue.1, pp.1-38, 1998.
DOI : 10.1016/S0377-0427(97)00190-8

. Pagès, Optimal Quantization Methods and Applications to Numerical Problems in Finance, Handbook of computational and numerical methods in finance, pp.253-297, 2004.
DOI : 10.1007/978-0-8176-8180-7_7

. Pakdaman, Fluid limit theorems for stochastic hybrid systems with application to neuron models, Advances in Applied Probability, vol.46, issue.03, pp.761-794, 2010.
DOI : 10.1073/pnas.0236032100
URL : https://hal.archives-ouvertes.fr/hal-00447808

M. G. Riedler, Almost sure convergence of numerical approximations for Piecewise Deterministic Markov Processes, Journal of Computational and Applied Mathematics, vol.239, 2011.
DOI : 10.1016/j.cam.2012.09.021

D. Vermes, Optimal control of piecewise deterministic markov process, Stochastics, vol.10, issue.3, pp.165-207, 1985.
DOI : 10.1080/17442508508833338

. Zeiser, Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes, Journal of Mathematical Biology, vol.2, issue.1, pp.207-246, 2010.
DOI : 10.1007/s00285-009-0264-9
URL : https://hal.archives-ouvertes.fr/hal-00470252