Markov property of point processes |
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Authors: | Hans G Kellerer |
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Institution: | 1. Mathematisches Institut der Universit?t München, Theresienstrasse 39, D-8000, München, Federal Republic of Germany
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Abstract: | Summary A point process
on R
+ can be represented by the associated counting process (ξ
t
;t∈
R
+) or by the associated sequence of jump times (τ
n
;n∈
Z
+) and in accordance may possess two types of Markov property. The present paper first clarifies their mutual dependence, leading
in particular to the notion of “weak multiplicativity” for the joint distribution of two consecutive jump times. Then, by
means of results from a previous paper, a uniquely determined “Markov variant”
is assigned to
without changing the one-dimensional marginals. This provides in particular a new characterization of the Poisson process
by these marginals and the adequate Markov property. Further applications concern the explicit construction of the compensator
and certain transition probabilities of
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Keywords: | |
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