Multiparameter Processes: An Introduction to Random Fields

✍ Scribed by Davar Khoshnevisan (auth.)

• Publisher: Springer-Verlag New York
• Year: 2002
• Tongue: English
• Leaves: 590
• Series: Springer Monographs in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xix
Front Matter....Pages 1-1
Discrete-Parameter Martingales....Pages 3-46
Two Applications in Analysis....Pages 47-63
Random Walks....Pages 65-104
Multiparameter Walks....Pages 105-136
Gaussian Random Variables....Pages 137-179
Limit Theorems....Pages 181-213
Front Matter....Pages 215-215
Continuous-Parameter Martingales....Pages 217-266
Constructing Markov Processes....Pages 267-312
Generation of Markov Processes....Pages 313-341
Probabilistic Potential Theory....Pages 343-389
Multiparameter Markov Processes....Pages 391-454
The Brownian Sheet and Potential Theory....Pages 455-495
Front Matter....Pages 497-497
Kolmogorov’s Consistency Theorem....Pages 499-500
Laplace Transforms....Pages 501-509
Hausdorff Dimensions and Measures....Pages 511-525
Energy and Capacity....Pages 527-541
Back Matter....Pages 543-584

✦ Subjects

Probability Theory and Stochastic Processes