On the maximum of a Wiener process and its location

E. Csáki, A. Földes, P. Révész

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Consider a Wiener process {W(t),t≧0}, let M(t)=max |W(s)| and v(t) be the location of the maximum of the absolute value of {Mathematical expression} in [0, t] i.e. |W(v(t))|=M(t). We study the limit points of (αtM(t),βtv(t)) as t→∞ where αt and βt are positive, decreasing normalizing constants. Moreover, a lim inf result is proved for the length of the longest flat interval of M(t).

Original languageEnglish
Pages (from-to)477-497
Number of pages21
JournalProbability Theory and Related Fields
Volume76
Issue number4
DOIs
Publication statusPublished - Dec 1 1987

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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