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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Markov processes with identical hitting probabilities


Author: Joseph Glover
Journal: Trans. Amer. Math. Soc. 275 (1983), 131-142
MSC: Primary 60J40; Secondary 31C15, 60J55
DOI: https://doi.org/10.1090/S0002-9947-1983-0678339-9
MathSciNet review: 678339
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Abstract: Let $ (X(t),{P^x})$ and $ (Y(t),{Q^x})$ be transient Hunt processes on a state space $ E$ satisfying the hypothesis of absolute continuity (Meyer's hypothesis (L)). Let $ T(K)$ be the first entrance time into a set $ K$, and assume $ {P^x}(T(K) < \infty) = {Q^x}(T(K) < \infty)$ for all compact sets $ K \subseteq E$. There exists a strictly increasing continuous additive functional of $ X(t),A(t)$, so that if $ T(t) = {\text{inf}}\{s:A(s) > t\} $, then $ (X(T(t)),{P^x})$ and $ (Y(t),{Q^x})$ have the same joint distributions. An analogous result is stated if $ X$ and $ Y$ are right processes (with an additional hypothesis). These theorems generalize the Blumenthal-Getoor-McKean Theorem and have interpretations in terms of potential theory.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0678339-9
Keywords: Transient Hunt process, time change, Blumenthal-Getoor-McKean Theorem, continuous additive functional, réduite
Article copyright: © Copyright 1983 American Mathematical Society