Günter Last

The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.

The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.

Eine integrierte Einführung in die Mathematik, die vom Konkreten zum Allgemeinen aufsteigt, auf Schubladen wie "Lineare Algebra'' und "Analysis'' verzichtet und die (fast) alle Beweise enthält. Als Leser kommen besonders Studierende des Wirtschaftsingenieurwesens und anderer naturwissenschaftlich-technischer Studiengänge sowie Studierende der Wirtschaftsmathematik und der Informatik infrage. Auch Studierende neuer Studiengänge wie Bachelor in Mathematik und sogar des klassischen Diplom-Studiengangs Mathematik werden das Buch mit Gewinn lesen. Die Darstellung ist exakt, aber weniger abstrakt.

Eine integrierte und inhaltlich neu strukturierte Einführung in die Höhere Mathematik, die vom Konkreten zum Allgemeinen aufsteigt, auf Schubladen wie "Lineare Algebra'' und "Analysis'' verzichtet und die (fast) alle Beweise enthält. Die Stochastik wird auch von Anfang an einbezogen. Als Leser kommen nicht nur Studierende der Wirtschaftswissenschaften, besonders des Wirtschaftsingenieurwesens, sondern auch Studierende der Wirtschaftsmathematik infrage. Auch Studierende neuer Studiengänge wie Bachelor in Mathematik und sogar des klassischen Diplomstudiengangs Mathematik werden das Buch mit Gewinn lesen. Im Vergleich zur ersten Auflage wurden einige Umstellungen und Ergänzungen, insbesondere im Kapitel Differentialrechnung, vorgenommen sowie zusätzliche Graphiken eingefügt.

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.