Set-indexed Brownian motion on increasing paths

Ely Merzbach; Arthur Yosef

doi:10.1007/s10959-008-0188-0

Set-indexed Brownian motion on increasing paths

Ely Merzbach
, Arthur Yosef

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove that a square-integrable set-indexed stochastic process is a set-indexed Brownian motion if and only if its projections on all the strict increasing continuous paths are one-parameter time-change Brownian motions. We present some applications.

Original language	English
Pages (from-to)	883-890
Number of pages	8
Journal	Journal of Theoretical Probability
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s10959-008-0188-0
State	Published - Oct 2009

Keywords

Brownian motion
Increasing path
Set-indexed process

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10.1007/s10959-008-0188-0

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KW - Set-indexed process

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Set-indexed Brownian motion on increasing paths

Abstract

Keywords

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