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 language | English |
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Pages (from-to) | 19-35 |
Number of pages | 17 |
Journal | Probability Theory and Related Fields |
Volume | 71 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1986 |
Externally published | Yes |