In this book we study Markov random functions of several variables.
What is traditionally meant by the Markov property for a random
process (a random function of one time variable) is connected to
the concept of the phase state of the process and refers to the
independence of the behavior of the process in the future from its
behavior in the past, given knowledge of its state at the present
moment. Extension to a generalized random process immediately
raises nontrivial questions about the definition of a suitable"
phase state," so that given the state, future behavior does not
depend on past behavior. Attempts to translate the Markov property
to random functions of multi-dimensional "time," where the role of
"past" and "future" are taken by arbitrary complementary regions in
an appro priate multi-dimensional time domain have, until
comparatively recently, been carried out only in the framework of
isolated examples. How the Markov property should be formulated for
generalized random functions of several variables is the principal
question in this book. We think that it has been substantially
answered by recent results establishing the Markov property for a
whole collection of different classes of random functions. These
results are interesting for their applications as well as for the
theory. In establishing them, we found it useful to introduce a
general probability model which we have called a random field. In
this book we investigate random fields on continuous time domains.
Contents CHAPTER 1 General Facts About Probability Distributions
1."
General
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