A limit law for random walk in a random environment

H. Kesten; M. V. Kozlov; F. Spitzer

Compositio Mathematica (1975)

  • Volume: 30, Issue: 2, page 145-168
  • ISSN: 0010-437X

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Kesten, H., Kozlov, M. V., and Spitzer, F.. "A limit law for random walk in a random environment." Compositio Mathematica 30.2 (1975): 145-168. <http://eudml.org/doc/89251>.

@article{Kesten1975,
author = {Kesten, H., Kozlov, M. V., Spitzer, F.},
journal = {Compositio Mathematica},
language = {eng},
number = {2},
pages = {145-168},
publisher = {Noordhoff International Publishing},
title = {A limit law for random walk in a random environment},
url = {http://eudml.org/doc/89251},
volume = {30},
year = {1975},
}

TY - JOUR
AU - Kesten, H.
AU - Kozlov, M. V.
AU - Spitzer, F.
TI - A limit law for random walk in a random environment
JO - Compositio Mathematica
PY - 1975
PB - Noordhoff International Publishing
VL - 30
IS - 2
SP - 145
EP - 168
LA - eng
UR - http://eudml.org/doc/89251
ER -

References

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  1. [1] K.B. Athreya and P.E. Ney: Branching processes. Springer Verlag, 1972. Zbl0259.60002MR373040
  2. [2] A.A. Chernov: Replication of a multicomponent chain by the lightning mechanism. Biofizika12 (1967) 297-301 = Biophysics 12 (1967) 336-341. 
  3. [3a] W. Feller: An introduction to probability theory and its applications, vol. I, 3rd ed., 1968. Zbl0158.34902MR228020
  4. [3b] W. Feller: An introduction to probability theory and its applications, vol. II, 2nd ed., 1971. Zbl0158.34902MR270403
  5. [4] B.V. Gnedenko and A.N. Kolmogorov: Limit distributions for sums of independent random variables. Addison-Wesley Publ. Co., 1954. Zbl0056.36001MR62975
  6. [5] H. Kesten: Random difference equations and renewal theory for products of random matrices. Acta Math.131 (1973) 208-248. Zbl0291.60029MR440724
  7. [6] M.V. Kozlov: A random walk on the line with stochastic structure. Teor. Veroyatnost i Primenen18 (1973) 406-408. Zbl0299.60054MR319274
  8. [7] P. Pyke and R. Schaufele: Limit theorems for Markov renewal processes. Ann. Math. Statist.35 (1964) 1746-1764. Zbl0134.34602MR168026
  9. [8] R.F. Serfozo: Functional limit theorems for stochastic processes based on embedded processes (to appear in Adv. Appl. Prob.). Zbl0323.60040MR402846
  10. [9] B.A. Sevastyanov: Branching processes. Izdatelstvo Nauka, 1971. 
  11. [10] F. Solomon: Random walks in a random environment, Ph.D. thesis, Cornell University, 1972, see also Ann. Prob.3 (1975) 1-31. Zbl0305.60029MR362503
  12. [11] D.E. Temkin: One dimensional random walks in a two-component chain. Dokl. Akad. Nauk SSSR206N1 (1972) 27-30 =Soviet Math.13 (1972) 1172-1176. Zbl0276.60067MR314119
  13. [12] J.V. Uspensky: Introduction to mathematical probability. McGraw Hill Book Co., 1937. JFM63.1069.01
  14. [13] H. Wittenberg: Limiting distributions of random sums of independent random variables. Z. Wahrscheinlichkeitstheorie verw. Geb.3 (1964) 7-18. Zbl0125.08601MR165549

Citations in EuDML Documents

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  1. Jonathon Peterson, Quenched limits for transient, ballistic, sub-gaussian one-dimensional random walk in random environment
  2. Nathanaël Enriquez, Christophe Sabot, Olivier Zindy, Aging and quenched localization for one-dimensional random walks in random environment in the sub-ballistic regime
  3. Nathanaël Enriquez, Christophe Sabot, Olivier Zindy, Limit laws for transient random walks in random environment on
  4. Eddy Mayer-Wolf, Alexander Roitershtein, Ofer Zeitouni, Limit theorems for one-dimensional transient random walks in Markov environments
  5. Nina Gantert, Jonathon Peterson, Maximal displacement for bridges of random walks in a random environment
  6. Elie Aidékon, Large deviations for transient random walks in random environment on a Galton–Watson tree
  7. Christophe Gallesco, Meeting time of independent random walks in random environment
  8. Jean-Pierre Conze, Yves Guivarc'h, Marches en milieu aléatoire et mesures quasi-invariantes pour un système dynamique
  9. Elena Kosygina, Thomas Mountford, Limit laws of transient excited random walks on integers
  10. Jonathon Peterson, Gennady Samorodnitsky, Weak quenched limiting distributions for transient one-dimensional random walk in a random environment

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