Previous article Next article Limit Theorems for Random Walks in Symmetric Random EnvironmentsA. O. GolosovA. O. Golosovhttps://doi.org/10.1137/1129037PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] D. E. Temkin, One-dimensional random walks in a two-component chain, Soviet Math. Doklady, 13 (1972), 1172–1176 0276.60067 Google Scholar[2] Fred Solomon, Random walks in a random environment, Ann. Probability, 3 (1975), 1–31 50:14943 0305.60029 CrossrefGoogle Scholar[3] H. Kesten, , M. V. Kozlov and , F. Spitzer, A limit law for random walk in a random environment, Compositio Math., 30 (1975), 145–168 52:1895 0388.60069 Google Scholar[4] G. Ritter, Masters Thesis, Random walk in a random environment, critical case, a thesis, Cornell Univ., Ithaca, NY, 1976 Google Scholar[5] Ya. G. Sinai, The limiting behavior of a one-dimensional random walk in a random medium, Theory Prob. Appl., 27 (1982), 256–268 LinkGoogle Scholar[6] J. Bernasconi, , W. R. Schneider and , W. Wyss, Diffusion and hopping conductivity in disordered one-dimensional lattice systems, Z. Physik B, 37 (1980), 175–184 CrossrefGoogle Scholar[7] S. Alexander, , J. Bernasconi, , W. R. Schneider and , R. Orbach, Excitation dynamics in random one-dimensional systems, Rev. Modern Phys., 53 (1981), 175–198 10.1103/RevModPhys.53.175 82d:82051 CrossrefGoogle Scholar[8] V. V. Anshelevich and , A. V. Vologodskii, Laplace operator and random walk on one-dimensional nonhomogeneous lattice, J. Statist. Phys., 25 (1981), 419–430 82k:82002 0512.60059 CrossrefGoogle Scholar[9] V. V. Anshelevich, , K. M. Khanin and , Ya. G. Sinai, Symmetric random walks in random environments, Comm. Math. Phys., 85 (1982), 449–470 84a:60082 0512.60058 CrossrefGoogle Scholar[10] William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons Inc., New York, 1966xviii+636 35:1048 0138.10207 Google Scholar[11] Walter A. Rosenkrantz and , C. C. Y. Dorea, Limit theorems for Markov processes via a variant of the Trotter-Kato theorem, J. Appl. Probab., 17 (1980), 704–715 81h:60041 0464.60034 CrossrefGoogle Scholar[12] Petr Mandl, Analytical treatment of one-dimensional Markov processes, Die Grundlehren der mathematischen Wissenschaften, Band 151, Academia Publishing House of the Czechoslovak Academy of Sciences, Prague, 1968xx+192 40:930 0179.47802 Google Scholar[13] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons Inc., New York, 1968xii+253 38:1718 0172.21201 Google Scholar[14] F. V. Atkinson, Discrete and continuous boundary problems, Mathematics in Science and Engineering, Vol. 8, Academic Press, New York, 1964xiv+570 31:416 0117.05806 Google Scholar[15] A. N. Kolomogorov, Foundations of the Theory of Probability, Chelsea, New York, 1956 Google Scholar[16] A. O. Golosov, Random walks in symmetric random media, Uspekhi Mat. Nauk, 38 (1983), 175–176, (In Russian.) 85c:60103 0538.60076 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 29, Issue 2| 1985Theory of Probability & Its Applications History Submitted:23 July 1982Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1129037Article page range:pp. 266-280ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics