Set-Indexed Martingales (Hardcover)

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.

General

Imprint:	Chapman & Hall/CRC
Country of origin:	United States
Series:	Chapman & Hall/CRC Monographs on Statistics and Applied Probability
Release date:	October 1999
First published:	1999
Authors:	B.G. Ivanoff
Series editors:	D.R. Cox
Authors:	Ely Merzbach
Series editors:	N. Reid • Valerie Isham • R.J. Tibshirani • Thomas A Louis • Howell Tong • Niels Keiding
Dimensions:	229 x 152 x 17mm (L x W x T)
Format:	Hardcover
Pages:	224
ISBN-13:	978-1-58488-082-0
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Mathematical foundations > Set theory Promotions
LSN:	1-58488-082-1
Barcode:	9781584880820

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