DISCRETE-PARAMETER RANDOM FIELDS Discrete Parameter Martingales Two Applications in Analysis Random Walks Multiparameter Walks Gaussian Random Walks Limit Theorems; CONTINUOUS-PARAMETER RANDOM FIELDS Continuous Parameter Martingales Constructing Markov Processes Generation of Markov Processes Probabilistic Potential Theory Multiparameter Markov Processes Brownian Sheet and Potential Theory; APPENDICES Kolmogorov's Consistency Theorem Laplace Transforms Hausdorff Dimensions and Measures Energy and Capacity
Self-contained presentation: from elementary material to state-of-the-art research; Much of the theory in book-form for the first time; Connections are made between probability and other areas of mathematics, engineering and mathematical physics
Multi-parameter processes extend the existing one-parameter theory in an elegant way and have many applications to other fields in mathematics. This book on random fields is designed for a second graduate course in probability. Recent work on random fields has made it possible to make it an expository subject which interacts with several other areas in mathematics and has enough mathematical depth to be of use to pure as well as applied mathematicians of many backgrounds.