Set-Indexed Martingales

Name: Set-Indexed Martingales
Brand: Taylor & Francis Inc
Price: 228.75 AUD
Availability: BackOrder

By: Ely Merzbach, Gail Ivanoff

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Hardcover | 27 October 1999 | Edition Number 1

At a Glance

Hardcover
224 Pages

Dimensions(cm)
24.1 x 16.0 x 1.7

Hardcover

RRP $263.00

$228.75

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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.

Industry Reviews

"a small, elegant volumeThis state-of-the-art monograph will be a valuable resource and stimulus for further work in the area." -Short Book Reviews of the ISI "I would recommend the book as an excellent introduction to set-indexed martingales. The foundations of the general theory are clearly presented and the reader is led to a point that is close to the current edge of research." --Simon Harris, University of Bath

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