Strong invariance for local times

E. Csáki, P. Révész

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29 Citations (Scopus)

Abstract

Let Y1, Y2, ... be a sequence of i.i.d. random variables with distribution P(Y1 = k) = pk (k = ±1, ±2,...), E(Y1) = 0, E(Y12) = σ2<∞. Put Tn = Y1+...+Yn and N(x,n) = # {k:0<k≦n, Tk = x}. Extending the result of Révész (1981) it is shown that for appropriate Skorohod construction we have {Mathematical expression} provided all moments E(|Y1|m), m≧0 exists where L is the local time of a Wiener process. Certain rate of convergence is given also under weaker conditions and for |L(x,nσ2)-σ2N(x, n)| too, when x is fixed.

Original languageEnglish
Pages (from-to)263-278
Number of pages16
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume62
Issue number2
DOIs
Publication statusPublished - Jun 1 1983

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ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Mathematics(all)

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