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On the Pathwise Comparison of Jump Processes Driven by Stochastic Intensities
Author(s) -
Brandt A.,
Last G.
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941670103
Subject(s) - mathematics , jump , representation (politics) , sequence (biology) , markov chain , space (punctuation) , pure mathematics , statistics , computer science , physics , quantum mechanics , politics , biology , political science , law , genetics , operating system
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.