Set-Indexed Martingales

Ivanoff, B. Gail; Merzbach, Ely; Ivanoff, Gail

ISBN 10: 1584880821 / ISBN 13: 9781584880820

Edité par Chapman and Hall/CRC, 1999

A propos de cet article

N° de réf. du vendeur 608176-n

Détails bibliographiques

• Titre: Set-Indexed Martingales
• Éditeur: Chapman and Hall/CRC
• Date de parution: 1999
• Langue: anglais
• ISBN à 10 chiffres: 1584880821
• ISBN à 13 chiffres: 9781584880820
• Reliure: Couverture rigide
• État de l'article: New

A propos de ce titre

Synopsis

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.

À propos de l?auteur

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.