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Teoriya Veroyatnostei i ee Primeneniya, 2004, Volume 49, Issue 3, Pages 601–609
DOI: https://doi.org/10.4213/tvp211 (Mi tvp211) 		 
This article is cited in 7 scientific papers (total in 7 papers)

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Unified limit theorems for increments of processes with independent increments

A. N. Frolov

Saint-Petersburg State University
Full-text PDF (1195 kB) Citations (7)
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DOI: https://doi.org/10.4213/tvp211
Abstract: A unified theory is constructed which describes the a.s. (almost surely) behavior of increments of stochastically continuous homogeneous processes with independent increments. This theory includes the strong law of large numbers, the Erdös–Rényi law, the Shepp law, the Csörgő–Révész law, and the law of the iterated logarithm. The range of applicability of the results is extended from several particular cases to the whole class of stochastically continuous homogeneous processes with independent increments.
Keywords: increments of processes with independent increments, Erdös–Rényi law, Shepp law, the law of large numbers, the law of the iterated logarithm.
Received: 23.05.2003
English version:
Theory of Probability and its Applications, 2005, Volume 49, Issue 3, Pages 531–540
DOI: https://doi.org/10.1137/S0040585X9798124X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. N. Frolov, “Unified limit theorems for increments of processes with independent increments”, Teor. Veroyatnost. i Primenen., 49:3 (2004), 601–609; Theory Probab. Appl., 49:3 (2005), 531–540
Citation in format AMSBIB
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\jour Theory Probab. Appl.
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  • https://www.mathnet.ru/eng/tvp/v49/i3/p601
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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