no. 5
Limit theorems for one-dimensional transient random walks in Markov environments
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 5, pp. 635-659. 
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     author = {Mayer-Wolf, Eddy and Roitershtein, Alexander and Zeitouni, Ofer},
     title = {Limit theorems for one-dimensional transient random walks in {Markov} environments},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {635--659},
     publisher = {Elsevier},
     volume = {40},
     number = {5},
     year = {2004},
     doi = {10.1016/j.anihpb.2004.01.003},
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     zbl = {1070.60024},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpb.2004.01.003/}
}
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Mayer-Wolf, Eddy; Roitershtein, Alexander; Zeitouni, Ofer. Limit theorems for one-dimensional transient random walks in Markov environments. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 5, pp. 635-659. doi : 10.1016/j.anihpb.2004.01.003. http://www.numdam.org/articles/10.1016/j.anihpb.2004.01.003/

[1] S. Alili, Asymptotic behavior for random walks in random environments, J. Appl. Probab. 36 (1999) 334-349. | MR | Zbl

[2] G. Alsmeyer, The Markov renewal theorem and related results, Markov Proc. Related Fields 3 (1997) 103-127. | MR | Zbl

[3] S. Asmussen, Applied Probability and Queues, Wiley, New York, 1987. | MR | Zbl

[4] K.B. Athreya, D. Mcdonald, P.E. Ney, Limit theorems for semi-Markov renewal theory for Markov chains, Ann. Probab. 6 (1978) 809-814. | MR | Zbl

[5] K.B. Athreya, P.E. Ney, A new approach to the limit theory of recurrent Markov chains, Trans. Amer. Math. Soc. 245 (1978) 493-501. | MR | Zbl

[6] K.B. Athreya, P.E. Ney, A renewal approach to the Perron-Frobenius theory of nonnegative kernels on general state spaces, Math. Z. 179 (1982) 507-529. | Zbl

[7] J. Bremont, On some random walks on Z in random medium, Ann. Probab. 30 (2002) 1266-1312. | MR | Zbl

[8] A.A. Chernov, Replication of a multicomponent chain by the “lightning mechanism”, Biophysics 12 (1967) 336-341.

[9] B. de Saporta, Tails of the stationary solution of the stochastic equation Yn+1=anYn+bn with Markovian coefficients, Stoch. Proc. Appl. (2004), in press. | Zbl

[10] R. Durrett, Probability: Theory and Examples, Duxbury Press, Belmont, 1996. | MR

[11] B.V. Gnedenko, A.N. Kolmogorov, Limit Distributions for Sums of Indpendent Random Variables, Addison-Wesley, Reading, MA, 1962. | MR | Zbl

[12] C.M. Goldie, Implicit renewal theory and tails of solutions of random equations, Ann. Appl. Probab. 1 (1991) 126-166. | MR | Zbl

[13] H. Kesten, M.V. Kozlov, F. Spitzer, A limit law for random walk in a random environment, Comp. Math. 30 (1975) 145-168. | Numdam | MR | Zbl

[14] H. Kesten, Random difference equations and renewal theory for products of random matrices, Acta. Math. 131 (1973) 208-248. | MR | Zbl

[15] H. Kesten, Renewal theory for functionals of a Markov chain with general state space, Ann. Probab. 2 (1974) 355-386. | MR | Zbl

[16] M. Kobus, Generalized Poisson distributions as limits of sums for arrays of dependent random vectors, J. Multivariate Anal. 52 (1995) 199-244. | MR | Zbl

[17] S.M. Kozlov, A random walk on the line with stochastic structure, Teoriya Veroyatnosti i Primeneniya 18 (1973) 406-408. | MR | Zbl

[18] S.A. Molchanov, Lectures on Random Media, in: Lecture Notes in Mathematics, vol. 1581, Springer, New York, 1994. | MR | Zbl

[19] E. Nummelin, General Irreducible Markov Chains and Non-negative Operators, Cambridge University Press, Cambridge, 1984. | MR | Zbl

[20] A. Roitershtein, One-dimensional linear recursions with Markov-dependent coefficients, 2004, in preparation.

[21] G. Samorodnitsky, M.S. Taqqu, Stable Non-Gaussian Random Processes, Chapman & Hall, 1994. | MR | Zbl

[22] V.M. Shurenkov, On the theory of Markov renewal, Theor. Probab. Appl. 29 (1984) 247-265. | MR | Zbl

[23] F. Solomon, Random walks in random environments, Ann. Probab. 3 (1975) 1-31. | MR | Zbl

[24] Z. Szewczak, On a central limit theorem for m-dependent sequences, Bull. Polish Acad. Sci. 36 (1988) 327-331. | MR | Zbl

[25] A.S. Sznitman, Topics in random walks in random environment, 2002. | Zbl

[26] C. Takacs, More randomness of environment does not always slow down a random walk, J. Theoret Probab. 14 (3) (2001) 699-715. | MR | Zbl

[27] D.E. Temkin, One-dimensional random walks in two-component chain, Soviet Math. Dokl. 13 (5) (1972) 1172-1176. | MR | Zbl

[28] O. Zeitouni, Random walks in random environment, in: XXXI Summer School in Probability, St. Flour, 2001, Lecture Notes in Math., vol. 1837, Springer, Berlin, 2004, pp. 193-312. | MR | Zbl

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