Sample function behavior of increasingprocesses with stationary, independent increments

Bert E. Fristedt

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

In this paper we are concerned with the sample functionsof increasing stochastic processes, Xv, having stationary, independent increments; normalized so that Xv has no deterministiclinear component and Xv(0) = 0, (i.e., Xv is a subordinator).two events:{ω: Xv(t, ω) > h(t) infinitely often as t →0}, {ω: Xu(tf ω) > h(t) infinitely often as t → ∞} .In case Xv is a stable process, Khinchin has given integraltests to apply to a wide class ofh's in order to decide whetherone, the other, or both of these two events have probability zeroor one. The purpose of this paper is to give similar results, without assuming X to be stable.

Original languageEnglish (US)
Pages (from-to)21-33
Number of pages13
JournalPacific Journal of Mathematics
Volume21
Issue number1
DOIs
StatePublished - Apr 1967
Externally publishedYes

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