G. Alsmeyer, A. Iksanov, and U. Rösler, On Distributional Properties of Perpetuities, Journal of Theoretical Probability, vol.117, issue.3, pp.666-682, 2009.
DOI : 10.1007/s10959-008-0156-8

G. K. Basak, A. Bisi, and M. K. Ghosh, Stability of a Random Diffusion with Linear Drift, Journal of Mathematical Analysis and Applications, vol.202, issue.2, pp.604-622, 1996.
DOI : 10.1006/jmaa.1996.0336

B. De-saporta, Tail of the stationary solution of the stochastic equation Yn+1 = anYn + bn with Markovian coefficients, Stochastic Process, Appl, vol.115, issue.12, pp.1954-1978, 2005.

B. De-saporta and J. Yao, Tail of a linear diffusion with Markov switching, The Annals of Applied Probability, vol.15, issue.1B, pp.992-1018, 2004.
DOI : 10.1214/105051604000000828
URL : https://hal.archives-ouvertes.fr/hal-00111278

N. Dunford and J. T. Schwartz, Linear operators. Part I, Wiley Classics Library General theory, With the assistance of William G. Bade and Robert G. Bartle, Reprint of the 1958 original, pp.47001-47005, 1988.

C. M. Goldie and R. Grübel, Perpetuities with thin tails, Advances in Applied Probability, vol.1, issue.02, pp.463-480, 1996.
DOI : 10.2307/1426858

X. Guyon, S. Iovleff, and J. Yao, Linear diffusion with stationary switching regime, ESAIM Probab, electronic). MR MR2085603, pp.25-35, 2004.

P. Hitsczenko and J. Weso-lowski, Perpetuities with thin tails revisited, The Annals of Applied Probability, vol.19, issue.6, pp.2080-2101, 2009.
DOI : 10.1214/09-AAP603

T. Kato, Perturbation theory for linear operators, Classics in Mathematics, vol.96, pp.47025-47029, 1995.

J. R. Norris, Markov chains, Cambridge Series in Statistical and Probabilistic Mathematics, 1997.
DOI : 10.1017/CBO9780511810633

C. Villani, Topics in optimal transportation, Graduate Studies in Mathematics, vol.58, pp.90003-90004, 2003.
DOI : 10.1090/gsm/058

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