Abstract
This chapter discusses stochastic Markovian fields. It also highlights generalized Markovian fields and Markovian sets. The first example of a Markovian field was the well-known Levy's Brownian motion with the multidimensional time, and until present, a number of general results have been achieved. The chapter explains a few classes of Markovian fields, in particular, stochastic fields arising as solutions of linear stochastic differential equations. A stochastic field on the vector space is called stationary (in the wide sense) if the correlation of its values does not change under the shift transformations of the parameter. The chapter also explores dual stochastic fields and Markov property.
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