Limit Theorems For Additive Functionals Research Articles

Discussion on the Meeting on the Gibbs Sampler and Other Markov Chain Monte Carlo Methods

Discussion on the Meeting on the Gibbs Sampler and Other Markov Chain Monte Carlo Methods

The exact order of the convergence rate in the central limit theorem for additive functions

The exact order of the convergence rate in the central limit theorem for additive functions

An ergodic theorem related to some limit theorems for additive functionals of complex Brownian motion

An ergodic theorem related to some limit theorems for additive functionals of complex Brownian motion

A Conditional Limit Theorem for Additive Functionals of a Random Walk

Previous article Next article A Conditional Limit Theorem for Additive Functionals of a Random WalkV. I. Afanas’evV. I. Afanas’evhttps://doi.org/10.1137/1135040PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] M. V. Kozlov, On the asymptotic behavior probability of nonextinction for critical branching processes in a random environment, Theory Probab. Appl., 21 (1976), 791–803 10.1137/1121091 0384.60058 LinkGoogle Scholar[2] William Feller, An introduction to probability theory and its applications. Vol. II, Second edition, John Wiley & Sons Inc., New York, 1971xxiv+669 42:5292 0219.60003 Google Scholar[3] Donald L. Iglehart, Random walks with negative drift conditioned to stay positive, J. Appl. Probability, 11 (1974), 742–751 51:4410 0302.60038 CrossrefGoogle Scholar[4] N. Veraverbeke and , J. L. Teugels, The exponential rate of convergence of the distribution of the maximum of a random walk, J. Appl. Probab., 12 (1975), 279–288, 13 (1976), pp. 733–740 0307.60061 CrossrefGoogle Scholar[5] W. D. Kaigh, A conditional local limit theorem for recurrent random walk, Ann. Probability, 3 (1975), 883–888 52:9337 0322.60064 CrossrefGoogle Scholar[6] V. I. Afanas'ev, On functionals of a random walk prior to first reaching until it the negative half-axis, Theory Probab. Appl., 3 (1986), 683–687 0658.60049 Google Scholar[7] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons Inc., New York, 1968xii+253 38:1718 0172.21201 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails On the behavior of the batch arrival queueMx/M/1 during a busy periodNaval Research Logistics, Vol. 41, No. 2 | 1 Mar 1994 Cross Ref Volume 35, Issue 2| 1991Theory of Probability & Its Applications205-409 History Submitted:30 March 1987Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1135040Article page range:pp. 330-336ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Nonuniform estimate in the central limit theorem for additive functions

Nonuniform estimate in the central limit theorem for additive functions

The central limit theorem for additive functionals of Markov and semi-Markov processes

One presents the results obtained recently by the collaborators of the Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, regarding limit theorems for additive functionals of Markov and semi-Markov processes. One makes use of the theory of inversion of singularly perturbed semigroups of operators in the phase extension scheme and of the methods of asymptotic analysis of singularly perturbed Markov renewal equations.

Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions

We prove a functional central limit theorem for additive functionals of stationary reversible ergodic Markov chains under virtually no assumptions other than the necessary ones. We use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk.

The central limit theorem for additive functionals of Markov processes and the weak convergence to Wiener measure

The central limit theorem for additive functionals of Markov processes and the weak convergence to Wiener measure

Integral Equations and Limit Theorems for Additive Functionals of a Markov Process

Integral Equations and Limit Theorems for Additive Functionals of a Markov Process