Overview
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.
Full Product Details
Author: B.G. Ivanoff (University of Ottawa, Ontario, Canada) ,
Ely Merzbach (Bar Ilan University, Ramat-Gan, Israel) ,
Ely Merzbach ,
N. Reid (University of Toronto, Ontario, Canada)
Publisher: Taylor & Francis Inc
Imprint: Chapman & Hall/CRC
Volume: 85
Dimensions:
Width: 15.20cm
, Height: 1.70cm
, Length: 22.90cm
Weight: 0.488kg
ISBN: 9781584880820
ISBN 10: 1584880821
Pages: 224
Publication Date: 27 October 1999
Audience:
College/higher education
,
Professional and scholarly
,
Undergraduate
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Active
Availability: In Print
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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
"""…a small, elegant volume…This 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"
Author Information
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.
