Geodesic
A criterion for linear drift, and the central limit theorem for one-dimensional random walks in a random environment
Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 73-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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A study is made of one-dimensional random walks in a random environment with bounded jumps in a unit of time (no more than $L$ to the left and no more than $R$ to the right, where $R$ and $L$ are positive integers). A criterion for linear drift is proved, along with the central limit theorem for such random walks in a random environment. 
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A. V. Letchikov. A criterion for linear drift, and the central limit theorem for one-dimensional random walks in a random environment. Sbornik. Mathematics, Tome 79 (1994) no. 1, pp. 73-92. http://geodesic.mathdoc.fr/item/SM_1994_79_1_a5/

[1] Key E., “Recurrence and transience criteria for random walk in a random environement”, Ann. Prob., 12:2 (1984), 529–560 | DOI | MR | Zbl

[2] Letchikov A. V., “Predelnaya teorema dlya vozvratnogo sluchainogo bluzhdaniya v sluchainoi srede”, DAN SSSR, 302:1 (1989), 25–28 | MR

[3] Letchikov A. V., “Localization of one-dimensional random walks in random environements”, Sov. Sci. Rev. Sec. C: Math. Phys., 8 (1989), 173–220 | MR | Zbl

[4] Letchikov A. V., “Limit theorems for one-dimensional random walks in random environements”, Prob. Th. and Math. Stat., 2 (1990), 90–96 | MR

[5] Letchikov A. V., “Asimptoticheskie svoistva odnomernykh sluchainykh bluzhdanii v sluchainoi srede s veroyatnostyu 1”, Matem. sb., 182:12 (1991), 1710–1728 | MR

[6] Revesz P., Random walk in random and nonrandom environments, World Sci. Publ. Co., Inc., Teack, N.Y., 1990 | MR | Zbl

[7] Solomon F., “Random walks in a random environement”, Ann. Prov., 3:1 (1975), 1–31 | DOI | MR | Zbl

[8] Sinai Ya. G., “Predelnoe povedenie odnomernogo sluchainogo bluzhdaniya v sluchainoi srede”, Teoriya veroyatnostei i ee primeneniya, 27:2 (1982), 247–258 | MR | Zbl

[9] Kesten H., Kozlov M. V., Spitzer F., “A limit law for random walk in a random environement”, Comp. Math., 30:2 (1975), 145–168 | MR | Zbl

[10] Letchikov A. V., “K resheniyu zadachi Kestena”, Teoriya veroyatnostei i ee primeneniya, 35:2 (1990), 358–361 | MR | Zbl

[11] Kesten H., “Random walk in random environement”, Contemp. Math., 50 (1984), 332

[12] Oseledets V. I., “Multiplikativnaya ergodicheskaya teorema. Kharakteristicheskie pokazateli Lyapunova dinamicheskikh sistem”, Tr. MMO, 19, URSS, M., 179–210 | Zbl

[13] Ibragimov I. A., Linnik Yu. V., Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965

[14] Lyubich Yu. I., Tabachnikov M. I., “Subgarmonicheskie funktsii na orientirovannom grafe”, Sib. matem. zhurn., 10:3 (1969), 600–608 | MR

[15] Chzhun K.-L., Odnorodnye tsepi Markova, Mir, M., 1964