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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 2, Pages 333–357
DOI: https://doi.org/10.4213/tvp57 (Mi tvp57) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Local invariance principle for independent and identically distributed random variables

J.-Ch. Bretona, Yu. A. Davydovb

a Université de La Rochelle
b University of Sciences and Technologies
Full-text PDF (1957 kB) Citations (2)
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DOI: https://doi.org/10.4213/tvp57
Abstract: It is well known that for a sequence of independent and identically distributed random variables, the corresponding normalized step-processes converge weakly to the Wiener process. A stronger convergence, namely the convergence in variation of the functional distributions of these processes, has been established in [Y. A. Davydov, M. A. Lifshits, and N. V. Smorodina, Local Properties of Distributions of Stochastic Functionals, American Mathematical Society, Providence, RI, 1998] under the finiteness of the Fisher information of the random variables. In this paper we prove such convergences without a Fisher information type condition.
Keywords: invariance principles, convergence in total variation, local limit theorems.
Received: 09.07.2002
Revised: 30.10.2003
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 2, Pages 256–278
DOI: https://doi.org/10.1137/S0040585X97982335
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Language: English
Citation: J.-Ch. Breton, Yu. A. Davydov, “Local invariance principle for independent and identically distributed random variables”, Teor. Veroyatnost. i Primenen., 51:2 (2006), 333–357; Theory Probab. Appl., 51:2 (2007), 256–278
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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