Set-Indexed Martingales
B.G. Ivanoff · Ely Merzbach
Dec 2024 · Taylor & Francis
Ebook
224
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About this ebook
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.
About the author
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.
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