MaPhySto
Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

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Funded by The Danish National Research Foundation

Graduate course on

Marked Point Processes and Piecewise Deterministic Processes

Lectures by Martin Jacobsen, University of Copenhagen

While visiting MaPhySto, Martin Jacobsen will give a series of lectures (2 times 2 hours per week) on Marked Point Processes and Piecewise Deterministic Processes (MPP's and PDP's).

Marked point processes describe events of different types (marks) occurring at separate instants in time. The distribution of a MPP is completely described through a predictable compensating measure, which also is used to describe the basic martingale structures for a MPP and to derive martingale characterization results. Adding suitable rules for describing a dynamical evolution in time between events leads to the concept of a piecewise deterministic process, with piecewise deterministic Markov processes (homogeneous or non-homogeneous) as the main example. The construction of PDP's from MPP's is performed in such a way that the two processes generate the same filtration, hence the martingale structure for the PDP is the same as that for the MPP.

The lectures treat the basics of MPP-theory using conditional hazard measures and jump probabilities. The martingale structure is discussed, including characterization results and likelihood martingales (Girsanov type theorems). When discussing PDP's the emphasis is on the Markovian case, with the Markov property derived from properties of the underlying MPP.

A number of examples wil be given, perhaps also of other types of processes that may not be MPP's or PDP's, but may be viewed as limits of sequences of processes of either type.

The lectures will take place in H2.28 on Tuesdays 12-14 and Fridays 13-15. The first lecture will be given Tuesday 20 October, 1998.

For more information, please contact MaPhySto at maphysto@mi.aau.dk.