This book gives a self-contained introduction to the dynamic
martingale approach to marked point processes (MPP). Based on the
notion of a compensator, this approach gives a versatile tool for
analyzing and describing the stochastic properties of an MPP. In
particular, the authors discuss the relationship of an MPP to its
compensator and particular classes of MPP are studied in great
detail. The theory is applied to study properties of dependent
marking and thinning, to prove results on absolute continuity of
point process distributions, to establish sufficient conditions for
stochastic ordering between point and jump processes, and to solve
the filtering problem for certain classes of MPPs.
General
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