On the variation distance for probability measures defined on a filtered space

Yu M. Kabanov*, R. Sh Liptser, A. N. Shiryaev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

Abstract

We study the distance in variation between probability measures defined on a measurable space (Ω, ℱ) with right-continuous filtration (ℱt)t≦0. To every pair of probability measures P and {Mathematical expression} an increasing predictable process {Mathematical expression} (called the Hellinger process) is associated. For the variation distance {Mathematical expression} between the restrictions of P and {Mathematical expression} to ℱT (T is a stopping time), lower and upper bounds are obtained in terms of h. For example, in the case when {Mathematical expression}, {Mathematical expression} In the cases where P and {Mathematical expression} are distributions of multivariate point processes, diffusion-type processes or semimartingales h are expressed explicitly in terms of given predictable characteristics.

Original languageEnglish
Pages (from-to)19-35
Number of pages17
JournalProbability Theory and Related Fields
Volume71
Issue number1
DOIs
StatePublished - Jan 1986
Externally publishedYes

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