<p>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.</p>

Marked Point Processes on the Real Line: The Dynamical Approach (Probability and Its Applications)

Science & Math

Last, Günter

Brandt, Andreas

Mathematics

Springer

One of the basic problems arising in the stochastic modeling of systems is the existence and uniqueness of stationary (limiting) distributions of system characteristics. This monograph presents the basic methods for treating an equation due to Borovkov, particularly for functions that appear in queueing theory and related topics as well as some results obtained by means of these methods for some stochastic models. Also considered are relationships among the stationary distributions related to continuous time and to certain embedded epochs, model continuity and insensitivity of stationary distributions concerning the form of the distribution functions of certain input characteristics.

Stationary Stochastic Models

Franken, Peter

Lisek, Bernd

wiley

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