 Point processes with finite-dimensional conditional probabilitiesSøren Asmussen and Mogens Bladt Stochastic Processes and their Applications, 1999, vol. 82, issue 1, 127-142 Abstract: We study the structure of point processes N with the property that the vary in a finite-dimensional space where [theta]t is the shift and the [sigma]-field generated by the counting process up to time t. This class of point processes is strictly larger than Neuts' class of Markovian arrival processes. On the one hand, it allows for more general features like interarrival distributions which are matrix-exponential rather than phase type, on the other the probabilistic interpretation is a priori less clear. Nevertheless, the properties are very similar. In particular, finite-dimensional distributions of interarrival times, moments, Laplace transforms, Palm distributions, etc., are shown to be given by two fundamental matrices C, D just as for the Markovian arrival process. We also give a probabilistic interpretation in terms of a piecewise deterministic Markov process on a compact convex subset of , whose jump times are identical to the epochs of N. Keywords: Markovian; arrival; process; Matrix-exponential; distribution; Palm; theory; Rational; Laplace; transform; Semi-group (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:82:y:1999:i:1:p:127-142 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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