Some asymptotic results related to the law of iterated logarithm for Brownian motion

Terence Chan

Research output: Contribution to journalArticle

Abstract

For 0<?<1, let {Mathematical expression}. The questions addressed in this paper are motivated by a result due to Strassen: almost surely, lim supt?8U?((t))=1-exp{-4(?-1)-1}. We show that Strassen's result is closely related to a large deviations principle for the family of random variables U?(t), t>0. Also, when ?=1, U?(t)?0 almost surely and we obtain some bounds on the rate of convergence. Finally, we prove an analogous limit theorem for discounted averages of the form {Mathematical expression} as ??0, where D is a suitable discount function. These results also hold for symmetric random walks. © 1995 Plenum Publishing Corporation.

Original languageEnglish
Pages (from-to)643-667
Number of pages25
JournalJournal of Theoretical Probability
Volume8
Issue number3
DOIs
Publication statusPublished - Jul 1995

Keywords

  • Law of iterated logarithm

Fingerprint Dive into the research topics of 'Some asymptotic results related to the law of iterated logarithm for Brownian motion'. Together they form a unique fingerprint.

Cite this