J. Bect, Processus de Markov diffusif par morceaux: outils analytiques et numériques, 2007.

J. Bect, A unifying formulation of the Fokker-Planck-Kolmogorov equation for general stochastic hybrid systems, Proceedings of the 17th IFAC World Congress, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00215938

J. Bect, H. Baili, and G. Fleury, Generalized Fokker-Planck equation for piecewise-diffusion processes with boundary hitting resets, Proceedings of the 17 th International Symposium on the Mathematical Theory of Networks and Systems, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00016373

J. Bect, Y. Phulpin, H. Baili, and G. Fleury, On the Fokker-Planck Equation for Stochastic Hybrid Systems: Application to a Wind Turbine Model, 2006 International Conference on Probabilistic Methods Applied to Power Systems
DOI : 10.1109/PMAPS.2006.360298

URL : https://hal.archives-ouvertes.fr/hal-00016375

K. Bichteler, J. Gravereaux, and J. Jacod, Malliavin Calculus for Processes with Jumps, 1987.

R. M. Blumenthal and R. K. Getoor, Markov Processes and Potential Theory, Pure and Applied Mathematics, vol.29, 1968.

M. L. Bujorianu and J. Lygeros, General stochastic hybrid systems: modelling and optimal control, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), pp.1872-1877, 2004.
DOI : 10.1109/CDC.2004.1430320

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.5998

M. L. Bujorianu and J. Lygeros, Toward a General Theory of Stochastic Hybrid Systems, Stochastic Hybrid Systems: Theory and Safety Critical Applications, pp.3-30, 2006.
DOI : 10.1007/11587392_1

M. L. Bujorianu, J. Lygeros, W. Glover, and G. Pola, A stochastic hybrid system modeling framework, HYBRIDGE, 2001.

D. L. Cohn, Measure Theory, Birkhäuser, 1980.

M. H. Davis, Piecewise-deterministic Markov processes, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.46, pp.353-388, 1984.
DOI : 10.1007/978-1-4899-4483-2_2

M. H. Davis, Markov Models and Optimization, 1993.
DOI : 10.1007/978-1-4899-4483-2

M. H. Everdij and H. A. Blom, Hybrid Petri Nets with Diffusion That Have Into-Mappings with Generalised Stochastic Hybrid Processes, Lecture Notes in Control and Information Sciences, vol.337, pp.31-63, 2006.
DOI : 10.1007/11587392_2

W. Feller, The Parabolic Differential Equations and the Associated Semi-Groups of Transformations, The Annals of Mathematics, vol.55, issue.3, pp.468-519, 1952.
DOI : 10.2307/1969644

W. Feller, Diffusion processes in one dimension. Transactions of the, pp.1-31, 1954.

C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 1985.

M. K. Ghosh, A. Arapostathis, and S. I. Marcus, Optimal Control of Switching Diffusions with Application to Flexible Manufacturing Systems, SIAM Journal on Control and Optimization, vol.31, issue.5, pp.1-23, 1992.
DOI : 10.1137/0331056

M. K. Ghosh, A. Arapostathis, and S. I. Marcus, Ergodic Control of Switching Diffusions, SIAM Journal on Control and Optimization, vol.35, issue.6, pp.1952-1988, 1997.
DOI : 10.1137/S0363012996299302

J. P. Hespanha, A model for stochastic hybrid systems with application to communication networks. Nonlinear Analysis: Theory, Methods and Applications, pp.1353-1383, 2005.

J. Hu, J. Lygeros, and S. Sastry, Towards a Theory of Stochastic Hybrid Systems, pp.160-173, 2000.
DOI : 10.1007/3-540-46430-1_16

N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, 1981.

V. Kontorovich and V. Lyandres, Dynamic systems with random structure: an approach to the generation of nonstationary stochastic processes, Journal of the Franklin Institute, vol.336, issue.6, pp.939-954, 1999.
DOI : 10.1016/S0016-0032(99)00011-3

J. Krystul, A. Bagchi, and H. A. Blom, Risk decomposition and assessment methods, HYBRIDGE, 2001.

C. , L. Bris, and P. Lions, Existence and uniqueness of solutions to Fokker?Planck type equations with irregular coefficients, Communications in Partial Differential Equations, vol.33, issue.7, pp.1272-1317, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00667315

J. M. Lee, Introduction to smooth manifolds. Number 218 in Graduate Texts in Mathematics, 2003.

I. Lubashevsky, R. Friedrich, R. Mahnke, A. Ushakov, and N. Kubrakov, Boundary singularities and boundary conditions for the Fokker- Planck equations, 2006.

R. Malhamé and C. Chong, Electric load model synthesis by diffusion approximation of a high-order hybrid-state stochastic system, IEEE Transactions on Automatic Control, vol.30, issue.9, pp.854-860, 1985.
DOI : 10.1109/TAC.1985.1104071

I. M. Mitchell, The Flexible, Extensible and Efficient Toolbox of??Level??Set Methods, Journal of Scientific Computing, vol.31, issue.3, pp.300-329, 2008.
DOI : 10.1007/s10915-007-9174-4

I. M. Mitchell and J. A. Templeton, A Toolbox of Hamilton-Jacobi Solvers for Analysis of Nondeterministic Continuous and Hybrid Systems, pp.480-494, 2005.
DOI : 10.1007/978-3-540-31954-2_31

G. Pola, M. L. Bujorianu, J. Lygeros, M. D. Di, and . Benedetto, Stochastic hybrid models: an overview with application to air traffic management, ADHS 03, IFAC Conference on Analysis and Design of Hybrid Systems, 2003.

W. Rudin, Function Analysis, 1973.

M. Sharpe, General Theory of Markov Processes, 1988.

J. B. Walsh and M. Weil, Repr??sentation de temps terminaux et applications aux fonctionnelles additives et aux syst??mes de L??vy, Annales scientifiques de l'E.N.S. 4 e série, pp.121-155, 1972.
DOI : 10.24033/asens.1222