Home | Contents | Submissions, editors, etc. | Login | Search | EJP
 Electronic Communications in Probability > Vol. 10 (2005) > Paper 25 open journal systems 


A Log-scale Limit Theorem for One-dimensional Random Walks in Random Environments

Alexander Roitershtein, University of British Columbia, Canada


Abstract
We consider a transient one-dimensional random walk X_n in random environment having zero asymptotic speed. For a class of non-i.i.d. environments we show that log X_n / log n converges in probability to a positive constant.


Full text: PDF

Pages: 244-253

Published on: December 13, 2005
Bibliography
  1. S. Alili. Asymptotic behavior for random walks in random environments. J. Appl. Prob. 36 (1999), 334-349. Math. Review MR1724844 (2000i:60120)
  2. W. Bryc and A. Dembo. Large deviations and strong mixing. Annal. Inst. H. Poincare - Prob. Stat. 32 (1996), 549-569. Math. Review MR1411271 (97k:60075)
  3. A. Dembo and O. Zeitouni. Large deviation techniques and applications, 2nd edition, Springer, New York, 1998. Math. Review MR1619036 (99d:60030)
  4. B. de Saporta. Tails of the stationary solution of the stochastic equation Y_{n+1}=a_n Y_n+b_n with Markovian coefficients, to appear in Stoch. Proc. Appl. Math. Review number not available.
  5. N. Gantert and Z.Shi. Many visits to a single site by a transient random walk in random environment, Stoch. Proc. Appl. 99 (2002), 159-176. Math. Review MR1901151 (2003h:60148)
  6. C. M. Goldie. Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab. 1 (1991), 126-166. Math. Review MR1097468 (93i:60118)
  7. O. V. Gulinsky and A. Yu. Veretennikov. Large Deviations for Discrete-Time Processes with Averaging, VSP, Utrecht, The Netherlands, 1993. Math. Review MR1360713 (97a:60043)
  8. H. Kesten. Random difference equations and renewal theory for products of random matrices. Acta. Math. 131 (1973), 208-248. Math. Review MR0440724 (55 #13595)
  9. H. Kesten, M. V. Kozlov, and F. Spitzer. A limit law for random walk in a random environment. Comp. Math. 30 (1975), 145--168. Math. Review MR0380998 (52 #1895)
  10. M. V. Kozlov. A random walk on the line with stochastic structure. Teoriya Veroyatnosti i Primeneniya 18 (1973), 406-408. Math. Review MR0319274 (47 #7818)
  11. E. Mayer-Wolf, A. Roitershtein, and O. Zeitouni. Limit theorems for one-dimensional transient random walks in Markov environments. Ann. Inst. H. Poincare - Prob. Stat. 40 (2004), 635-659. Math. Review MR2086017 (2005g:60165)
  12. F. Solomon. Random walks in random environments. Annal. Probab. 3 (1975), 1-31. Math. Review MR0362503 (50 #14943)
  13. O. Zeitouni. Random walks in random environment. XXXI Summer School in Probability, St. Flour (2001). Lecture Notes in Math. 1837, Springer, 2004, 193-312. Math. Review MR2071631 (2006a:60201)
















Research
Support Tool
Capture Cite
View Metadata
Printer Friendly
Context
Author Address
Action
Email Author
Email Others


Home | Contents | Submissions, editors, etc. | Login | Search | EJP

Electronic Communications in Probability. ISSN: 1083-589X