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Introduction to Random Fields

  • David Griffeath
Part of the Graduate Texts in Mathematics book series (GTM, volume 40)

Abstract

One means of generalizing denumerable stochastic processes {x n } with time parameter set ℕ = {0, 1, ... } is to consider random fields {x t }, where t takes on values in an arbitrary countable parameter set T. Roughly, a random field with denumerable state space S is described by a probability measure μ on the space Ω = S T of all configurations of values from S on the generalized time set T. In this chapter we discuss certain extensions of Markov chains, called Markov fields which have been important objects of study in the recent development of probability theory. Only some of the highlights of this rich theory will be covered; we concentrate especially on the case T = ℤ = the integers, where the connections with classical Markov chain theory are deepest.

Keywords

Markov Chain Markov Process Random Field Transition Matrix Neighbor System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • David Griffeath

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