✦ LIBER ✦

On the Pathwise Comparison of Jump Processes Driven by Stochastic Intensities

✍ Scribed by A. Brandt; G. Last

Book ID: 102940201
Publisher: John Wiley and Sons
Year: 1994
Tongue: English
Weight: 947 KB
Volume: 167
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19941670103

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this paper we present a pathwise comparison theorem for jump processes governed by stochastic intensities and taking values in an arbitrary partially ordered Polish space. This generalizes recent results for the real‐valued case. The proof given here is based on competing risk arguments rather than on thinning and allows to avoid additional domination conditions. For real valued processes we obtain an almost sure pathwise representation of the comparison result based on an i.i.d. sequence of (0, 1)‐uniformly distributed random variables. For Markov chains our conditions coincide with the classical comparison conditions.

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