Acta mathematica scientia, Series B >
LYAPOUNOV EXPONENTS AND LAW OF LARGE NUMBERS FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES
Received date: 2006-12-06
Revised date: 2007-09-24
Online published: 2009-09-20
Supported by
Sponsored by the NSFC (10531070) and Research Foundation for Outstanding Young Teachers of China University of Geoscience (Wuhan) (0816)
In this article, the authors mainly discuss the law of large number under Kalikow's condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.
MAO Ming-Zhi , HAN Dong . LYAPOUNOV EXPONENTS AND LAW OF LARGE NUMBERS FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES[J]. Acta mathematica scientia, Series B, 2009 , 29(5) : 1383 -1394 . DOI: 10.1016/S0252-9602(09)60111-9
[1] Dembo A, Gantert N, Zeitouni O. Large deviations for random walk in random environment with holding times. Ann Probab, 2004, 32B(1): 996--1029
[2] Solomn F. Random walks in a environment. Ann Probab, 1975, 3: 1--31
[3] Kozlov S M. The method of averaging and walks in inhomogeneous environments. Russian Math Surv, 1985, 40: 73--145
[4] Greven A, Den Hollander F. Large deviations for a random environment. Ann Probab, 1994, 22: 1381--1428
[5] Hughes B D. Random Walks and Random Environments. Oxford: University Press, 1996
[6] Dembo A, Gantert N, Zeitouni O. Large deviation for random walks in random mixing environment. Ann Probab, 2004, 32: 880--914
[7] Varadhan S R S. Large deviations for random walks in a random environment. Comm Pure Appl Math, 2003, 56: 1222--1245
[8] Zeitouni O. Random walks in random environment. XXXI Summer school in probability St Flour, 2001. Lecture Notes in Math. Berlin: Springer-Verlag, 2004, 1837: 189--312
[9] Zeitouni O. Random walks in random environment. J Phys A, Math Gen, 2006, 39
[10] Mao Mingzhi, Han Dong. Asymptotic behavior for random walk in random environment with holding times. Chinese Journal of Applied Probability and Statistics, 2008, (2): 131--140
[11] Kalikow S A. Generalized random walk in a random environment. Ann Probab, 1981, 9: 753--768
[12] Sznitman A S, Zerner M P W. A law of large numbers for random walks in random environment. Ann Probab, 1999, 27(4): 1852--1869
[13] Liggett T. Interacting Particle Systems. New York: Springer--Verlag, 1985
[14] Zerner M P W. Directional decay of the Green's function for a random nonnegative potential on Zd. Ann Appl Probab, 1998, 8: 246--280
[15] Zerner M P W. Lyapounov exponents and quenched large deviations for mutlidimensional random walk in random environment. Ann Probab, 1998, 26: 1446--1476
[16] Sznitman A S. Shape theorem, Lyapounov exponents and large deviations for Brownian motion in a Poissonian potential. Comm Pure Appl Math, 1994, 47: 1655--1688
[17] Zerner M P W. Velocity and Lyapounov exponents of some random walks in random environment. Ann De L'I H Pro, (B), 2000, 36: 737--748
[18] Hu Dihe, Hu Xiaoyu. The construction of denumerable q-processes in random environments-the existence and uniqueness. Acta Mathematica Scientia, 2008, 28B(2): 225--235
[19] Sznitman A S. Brownian Motion, Obstacles and Random Media. Berlin: Springer--Verlag, 1998
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