Multiparameter Processes: An Introduction to Random Fields

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Springer Science & Business Media, Apr 10, 2006 - Mathematics - 584 pages
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.
 

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Contents

Two Applications in Analysis
47
Random Walks
65
Multiparameter Walks
105
Gaussian Random Variables
137
Limit Theorems 181
180
ContinuousParameter Random Fields
215
Stochastic Partial Differential Equations
255
Constructing Markov Processes
267
Multiparameter Markov Processes 391
390
The Brownian Sheet and Potential Theory
455
A Kolmogorovs Consistency Theorem 499
498
Hausdorff Dimensions and Measures
511
Energy and Capacity 527
526
References
543
Name Index
566
Subject Index
572

Generation of Markov Processes
313
Probabilistic Potential Theory
343

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