Previous article Next article On Probabilities of Small Deviations for Compound Renewal ProcessesA. N. Frolov, A. I. Martikainen, and J. SteinebachA. N. Frolov, A. I. Martikainen, and J. Steinebachhttps://doi.org/10.1137/S0040585X97983043PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe asymptotic behavior of small deviation probabilities for compound renewal processes is investigated.[1] A. A. Borovkov and and A. A. Mogulskii, On probabilities of small deviations for stochastic processes, Sib. Adv. Math., 1 (1991), pp. 39–63. Google Scholar[2] P. Embrechts and and C. Klüppelberg, Some aspects of insurance mathematics, Theory Probab. Appl., 38 (1994), pp. 262–295. TPRBAU 0040-585X LinkGoogle Scholar[3] Google Scholar[4] Google Scholar[5] Google Scholar[6] A. A. Mogul'skii, Small deviations in a space of trajectories, Theory Probab. Appl., 19 (1974), pp. 726–736. TPRBAU 0040-585X LinkGoogle Scholar[7] Google Scholar[8] Google ScholarKeywordssmall deviation probabilitiesrenewal processcompound Poisson processChung's law of the iterated logarithm Previous article Next article FiguresRelatedReferencesCited ByDetails On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent VariablesVestnik St. Petersburg University, Mathematics, Vol. 51, No. 3 | 4 September 2018 Cross Ref Volume 52, Issue 2| 2008Theory of Probability & Its Applications181-370 History Submitted:12 December 2005Published online:06 June 2008 InformationCopyright © 2008 Society for Industrial and Applied MathematicsKeywordssmall deviation probabilitiesrenewal processcompound Poisson processChung's law of the iterated logarithmPDF Download Article & Publication DataArticle DOI:10.1137/S0040585X97983043Article page range:pp. 328-337ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics