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Mathematics Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes
Posted on 2010-03-17
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The focus is on point processes that generate only finitely many points in finite time intervals, resulting, in particular, in piecewise deterministic processes with "few jumps." The point processes are constructed from scratch and their distributions characterized using compensating measures and martingale structures. Piecewise deterministic processes are defined and identified with certain marked point processes, and this identification is used to construct and study a large class of piecewise deterministic Markov processes, whether time homogeneous or not. The second part of the book shows how the theory developed earlier is used to analyze various models in statistics and applied probability with examples from survival analysis, branching processes, risk theory, finance, queueing theory and sports (soccer). Graduate students, postdocs and researchers in the above-mentioned areas will find this text an excellent resource, requiring only a solid foundation in probability theory and measure theory as well as basic knowledge of stochastic processes and martingales.
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