Lower functions for processes with stationary independent increments

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10 Citations (Scopus)

Abstract

Let {Xt} be a R1-valued process with stationary independent increments and {Mathematical expression}. In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing function h(t) such that lim inf At/h(t)=C a.s. as t→0 and t→∞, for some positive finite constant C when h(t) takes a particular form. Also two analytic conditions are considered as application.

Original languageEnglish
Pages (from-to)551-566
Number of pages16
JournalProbability Theory and Related Fields
Volume77
Issue number4
DOIs
Publication statusPublished - 1988 Dec

ASJC Scopus subject areas

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

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