Strong approximation of additive functionals

E. Csáki, M. Csörgo, A. Földes, P. Révész

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

Let X1, X2,...be a sequence of i.i.d. random variables and put S0=0, Sn=X1+...+Xn. A strong approximation type result is given for AN=∑i=1Nf(Si) where F(x), x∈R is a real valued function. A similar result is given for ∫0tg(B(s))ds. Some weak convergence type implications are also discussed.

Original languageEnglish
Pages (from-to)679-706
Number of pages28
JournalJournal of Theoretical Probability
Volume5
Issue number4
DOIs
Publication statusPublished - Oct 1992

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Additive Functionals
Strong Approximation
I.i.d. Random Variables
Weak Convergence
Weak convergence
Approximation
Random variables

Keywords

  • Additive functional
  • local time
  • random walk
  • strong approximation
  • Wiener process

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)

Cite this

Strong approximation of additive functionals. / Csáki, E.; Csörgo, M.; Földes, A.; Révész, P.

In: Journal of Theoretical Probability, Vol. 5, No. 4, 10.1992, p. 679-706.

Research output: Contribution to journalArticle

Csáki, E. ; Csörgo, M. ; Földes, A. ; Révész, P. / Strong approximation of additive functionals. In: Journal of Theoretical Probability. 1992 ; Vol. 5, No. 4. pp. 679-706.
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