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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 2, Pages 333–357 (Mi tvp57)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.

DOI: https://doi.org/10.4213/tvp57

Full text: PDF file (1957 kB)
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English version:
Theory of Probability and its Applications, 2007, 51:2, 256–278

Bibliographic databases:

Received: 09.07.2002
Revised: 30.10.2003
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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Joulin A., “On maximal inequalities for stable stochastic integrals”, Potential Anal., 26:1 (2007), 57–78  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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