Gail Ivanoff, Ely Merzbach

Set-Indexed Martingales (eBook, ePUB)

• Format: ePub

Produktbeschreibung

Set-Indexed Martingales offers a unique, comprehensive development of a general theory of Martingales indexed by a family of sets. The authors establish-for the first time-an appropriate framework that provides a suitable structure for a theory of Martingales with enough generality to include many interesting examples.

Developed from first principles, the theory brings together the theories of Martingales with a directed index set and set-indexed stochastic processes. Part One presents several classical concepts extended to this setting, including: stopping, predictability, Doob-Meyer decompositions, martingale characterizations of the set-indexed Poisson process, and Brownian motion. Part Two addresses convergence of sequences of set-indexed processes and introduces functional convergence for processes whose sample paths live in a Skorokhod-type space and semi-functional convergence for processes whose sample paths may be badly behaved.

Completely self-contained, the theoretical aspects of this work are rich and promising. With its many important applications-especially in the theory of spatial statistics and in stochastic geometry- Set Indexed Martingales will undoubtedly generate great interest and inspire further research and development of the theory and applications.

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Produktdetails

• Verlag: Taylor & Francis
• Erscheinungstermin: 15. Dezember 2024
• Englisch
• ISBN-13: 9781351416801
• Artikelnr.: 72484229

Autorenporträt

Gail Ivanoff, Professor of Mathematics and Statistics, University of Ottawa, Ontario, Canada. Ely Merzbach, Professor of Mathematics and Computer Science, Bar-Ilan University, Ramat Gan, Israel.