On the Asymptotic Behavior of Local Times of Recurrent Random Walks with Finite Variance

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Previous article Next article On the Asymptotic Behavior of Local Times of Recurrent Random Walks with Finite VarianceA. N. BorodinA. N. Borodinhttps://doi.org/10.1137/1126082PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Kiyoshi Itô and , H. McKean, Diffusion processes and their sample paths, Die Grundlehren der Mathematischen Wissenschaften, Band 125, Academic Press Inc., Publishers, New York, 1965xvii+321 33:8031 0127.09503 CrossrefGoogle Scholar[2] William Feller, Fluctuation theory of recurrent events, Trans. Amer. Math. Soc., 67 (1949), 98–119 11,255c 0039.13301 CrossrefGoogle Scholar[3] A. V. Skorokhod and , N. P. Slobodenyuk, Limit Theorems for Rondom Walks, Naukova Dumka, Kiev, 1970, 304–, (In Russian.) Google Scholar[4] I. McKean, Stochastic Integrals, Mir, Moscow, 1972, (Russian translation.) 0263.60021 Google Scholar[5] A. N. 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Math., 32 (1979), 721–747 81j:60080 0418.60074 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Scaling and local limits of Baxter permutations and bipolar orientations through coalescent-walk processesThe Annals of Probability, Vol. 50, No. 4 | 1 Jul 2022 Cross Ref Functional limit theorem for the local time of stopped random walkDiscrete Mathematics and Applications, Vol. 30, No. 3 | 25 Jun 2020 Cross Ref Convergence to the local time of Brownian meanderDiscrete Mathematics and Applications, Vol. 29, No. 3 | 26 Jun 2019 Cross Ref Scaling Limit for the Ant in High-Dimensional LabyrinthsCommunications on Pure and Applied Mathematics, Vol. 72, No. 4 | 26 January 2019 Cross Ref Функциональная предельная теорема для локального времени остановленного случайного блужданияДискретная математика, Vol. 31, No. 1 | 1 Jan 2019 Cross Ref Relative complexity of random walks in random scenery in the absence of a weak invariance principle for the local timesThe Annals of Probability, Vol. 45, No. 4 | 1 Jul 2017 Cross Ref Сходимость к локальному времени броуновской извилиныДискретная математика, Vol. 29, No. 4 | 1 Jan 2017 Cross Ref A functional limit theorem for excited random walksElectronic Communications in Probability, Vol. 22, No. none | 1 Jan 2017 Cross Ref Genealogies in expanding populationsThe Annals of Applied Probability, Vol. 26, No. 6 | 1 Dec 2016 Cross Ref Diffusion through thin membranes: Modeling across scalesPhysical Review E, Vol. 93, No. 4 | 12 April 2016 Cross Ref A uniform law for convergence to the local times of linear fractional stable motionsThe Annals of Applied Probability, Vol. 26, No. 1 | 1 Feb 2016 Cross Ref Limit theorems for random walks that avoid bounded sets, with applications to the largest gap problemStochastic Processes and their Applications, Vol. 125, No. 5 | 1 May 2015 Cross Ref A class of asymptotically self-similar stable processes with stationary incrementsStochastic Processes and their Applications, Vol. 124, No. 12 | 1 Dec 2014 Cross Ref Weak Invariance Principle for the Local Times of Partial Sums of Markov ChainsJournal of Theoretical Probability, Vol. 27, No. 2 | 9 August 2012 Cross Ref Scaling limits via excursion theory: Interplay between Crump–Mode–Jagers branching processes and processor-sharing queuesThe Annals of Applied Probability, Vol. 23, No. 6 | 1 Dec 2013 Cross Ref Relative complexity of random walks in random sceneriesThe Annals of Probability, Vol. 40, No. 6 | 1 Nov 2012 Cross Ref A scaling analysis of a cat and mouse Markov chainThe Annals of Applied Probability, Vol. 22, No. 2 | 1 Apr 2012 Cross Ref Large deviations for intersection local times in critical dimensionThe Annals of Probability, Vol. 38, No. 2 | 1 Mar 2010 Cross Ref Convergence of simple random walks on random discrete trees to Brownian motion on the continuum random treeAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 44, No. 6 | 1 Dec 2008 Cross Ref One-dimensional stepping stone models, sardine genetics and Brownian local timeThe Annals of Applied Probability, Vol. 18, No. 1 | 1 Feb 2008 Cross Ref Random rewards, fractional Brownian local times and stable self-similar processesThe Annals of Applied Probability, Vol. 16, No. 3 | 1 Aug 2006 Cross Ref A note on the weak invariance principle for local timesStatistics & Probability Letters, Vol. 32, No. 2 | 1 Mar 1997 Cross Ref Une preuve standard du principe d’invariance de stollSéminaire de Probabilités XXXI | 28 April 2008 Cross Ref The diffusive phase of a model of self-interacting walksProbability Theory and Related Fields, Vol. 103, No. 3 | 1 Sep 1995 Cross Ref Strong approximations to Brownian Local TimeSeminar on Stochastic Processes, 1992 | 1 Jan 1993 Cross Ref Local times on curves and uniform invariance principlesProbability Theory and Related Fields, Vol. 92, No. 4 | 1 Dec 1992 Cross Ref Self-intersections of 1-dimensional random walksProbability Theory and Related Fields, Vol. 72, No. 4 | 1 Jul 1986 Cross Ref On strong invariance for local time of partial sumsStochastic Processes and their Applications, Vol. 20, No. 1 | 1 Jul 1985 Cross Ref The Asymptotic Behavior of Local Times of Recurrent Random Walks with Infinite VarianceA. N. BorodinTheory of Probability & Its Applications, Vol. 29, No. 2 | 17 July 2006AbstractPDF (1264 KB)Limit Theorems for Sums of Independent Random Variables Defined on a Recurrent Random WalkA. N. BorodinTheory of Probability & Its Applications, Vol. 28, No. 1 | 17 July 2006AbstractPDF (1432 KB) Volume 26, Issue 4| 1982Theory of Probability & Its Applications657-870 History Submitted:16 April 1980Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1126082Article page range:pp. 758-772ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics