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Multiparameter Processes
ISBN-13:
9780387216317
Veröffentl:
2006
Seiten:
584
Autor:
Davar Khoshnevisan
Serie:
Springer Monographs in Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
Multiparameter processes extend the existing one-parameter theory of random processes in an elegant way, and have found connections to diverse disciplines such as probability theory, real and functional analysis, group theory, analytic number theory, and group renormalization in mathematical physics, to name a few.This book lays the foundation of aspects of the rapidly-developing subject of random fields, and is designed for a second graduate course in probability and beyond. Its intended audience is pure, as well as applied, mathematicians.Davar Khoshnevisan is Professor of Mathematics at the University of Utah. His research involves random fields, probabilistic potential theory, and stochastic analysis.
Discrete-Parameter Random Fields.- Discrete-Parameter Martingales.- Two Applications in Analysis.- Random Walks.- Multiparameter Walks.- Gaussian Random Variables.- Limit Theorems.- Continuous-Parameter Random Fields.- Continuous-Parameter Martingales.- Constructing Markov Processes.- Generation of Markov Processes.- Probabilistic Potential Theory.- Multiparameter Markov Processes.- The Brownian Sheet and Potential Theory.
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