References

• Alsmeyer, Gerold; Iksanov, Alex; Rösler, Uwe. On distributional properties of perpetuities. J. Theoret. Probab. 22 (2009), no. 3, 666--682. MR2530108
• Y. Bakhtin and T. Hurth. Invariant densities for dynamical systems with random switching, Preprint available on arXiv, 2012.
• Bardet, Jean-Baptiste; Guérin, Hélène; Malrieu, Florent. Long time behavior of diffusions with Markov switching. ALEA Lat. Am. J. Probab. Math. Stat. 7 (2010), 151--170. MR2653702
• J.B. Bardet, A. Christen, A. Guillin, A. Malrieu, and P.-A. Zitt, Total variation estimates for the TCP process, Preprint available on arXiv, 2012.
• M. Benaïm, S. Le~Borgne, F. Malrieu, and P.-A. Zitt. On the ergodicity of some piecewise deterministic markov processes, preprint, 2012.
• M. Benaïm, S. Le~Borgne, F. Malrieu, and P.-A. Zitt. On the stability of planar randomly switched systems, preprint, 2012.
• Boxma, Onno; Kaspi, Haya; Kella, Offer; Perry, David. On/off storage systems with state-dependent input, output, and switching rates. Probab. Engrg. Inform. Sci. 19 (2005), no. 1, 1--14. MR2104547
• E. Buckwar and M. G. Riedler. An exact stochastic hybrid model of excitable membranes including spatio-temporal evolution, J. Math. Biol. 63 (2011), no. 6, 1051--1093.
• Caputo, Pietro; Dai Pra, Paolo; Posta, Gustavo. Convex entropy decay via the Bochner-Bakry-Emery approach. Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009), no. 3, 734--753. MR2548501
• Chafaï, Djalil; Malrieu, Florent; Paroux, Katy. On the long time behavior of the TCP window size process. Stochastic Process. Appl. 120 (2010), no. 8, 1518--1534. MR2653264
• Costa, O. L. V. Stationary distributions for piecewise-deterministic Markov processes. J. Appl. Probab. 27 (1990), no. 1, 60--73. MR1039184
• Costa, O. L. V.; Dufour, F. Ergodic properties and ergodic decompositions of continuous-time Markov processes. J. Appl. Probab. 43 (2006), no. 3, 767--781. MR2274799
• Costa, O. L. V.; Dufour, F. Stability and ergodicity of piecewise deterministic Markov processes. SIAM J. Control Optim. 47 (2008), no. 2, 1053--1077. MR2385873
• Davis, M. H. A. Piecewise-deterministic Markov processes: a general class of nondiffusion stochastic models. With discussion. J. Roy. Statist. Soc. Ser. B 46 (1984), no. 3, 353--388. MR0790622
• Davis, M. H. A. Markov models and optimization. Monographs on Statistics and Applied Probability, 49. Chapman & Hall, London, 1993. xiv+295 pp. ISBN: 0-412-31410-X MR1283589
• de Saporta, Benoîte; Yao, Jian-Feng. Tail of a linear diffusion with Markov switching. Ann. Appl. Probab. 15 (2005), no. 1B, 992--1018. MR2114998
• Diaconis, Persi; Freedman, David. Iterated random functions. SIAM Rev. 41 (1999), no. 1, 45--76. MR1669737
• Dufour, François; Costa, Oswaldo L. V. Stability of piecewise-deterministic Markov processes. SIAM J. Control Optim. 37 (1999), no. 5, 1483--1502 (electronic). MR1710229
• Dumas, Vincent; Guillemin, Fabrice; Robert, Philippe. A Markovian analysis of additive-increase multiplicative-decrease algorithms. Adv. in Appl. Probab. 34 (2002), no. 1, 85--111. MR1895332
• J. Fontbona, H. Guérin, and F. Malrieu. Quantitative estimates for the long time behavior of a PDMP describing the movement of bacteria, arXiv, 2010.
• Goldie, Charles M.; Grübel, Rudolf. Perpetuities with thin tails. Adv. in Appl. Probab. 28 (1996), no. 2, 463--480. MR1387886
• Graham, Carl; Robert, Philippe. Interacting multi-class transmissions in large stochastic networks. Ann. Appl. Probab. 19 (2009), no. 6, 2334--2361. MR2588247
• Graham, Carl; Robert, Philippe. Self-adaptive congestion control for multi-class intermittent connections in a communication network, arXiv, 2010.
• Guyon, Xavier; Iovleff, Serge; Yao, Jian-Feng. Linear diffusion with stationary switching regime. ESAIM Probab. Stat. 8 (2004), 25--35 (electronic). MR2085603
• Hitczenko, Paweł; Wesołowski, Jacek. Perpetuities with thin tails revisited. Ann. Appl. Probab. 19 (2009), no. 6, 2080--2101. MR2588240
• Kesten, Harry. Random difference equations and renewal theory for products of random matrices. Acta Math. 131 (1973), 207--248. MR0440724
• Pakdaman, K.; Thieullen, M.; Wainrib, G. Fluid limit theorems for stochastic hybrid systems with application to neuron models. Adv. in Appl. Probab. 42 (2010), no. 3, 761--794. MR2779558
• Rachev, Svetlozar T. Probability metrics and the stability of stochastic models. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons, Ltd., Chichester, 1991. xiv+494 pp. ISBN: 0-471-92877-1 MR1105086
• O. Radulescu, A. Muller, and A. Crudu, Théorèmes limites pour des processus de Markov à sauts. Synthèse des résultats et applications en biologie moléculaire, Technique et Science Informatiques 26 (2007), no. 3-4, 443--469.
• Saloff-Coste, Laurent. Lectures on finite Markov chains. Lectures on probability theory and statistics (Saint-Flour, 1996), 301--413, Lecture Notes in Math., 1665, Springer, Berlin, 1997. MR1490046
• Vervaat, Wim. On a stochastic difference equation and a representation of nonnegative infinitely divisible random variables. Adv. in Appl. Probab. 11 (1979), no. 4, 750--783. MR0544194
• Villani, Cédric. Topics in optimal transportation. Graduate Studies in Mathematics, 58. American Mathematical Society, Providence, RI, 2003. xvi+370 pp. ISBN: 0-8218-3312-X MR1964483