A class of multidimensional random fields of Markov type. (English. Russian original) Zbl 0629.60057

Malyarenko, A. A.

Theory Probab. Math. Stat. 34, 109-115 (1987); translation from Teor. Veroyatn. Mat. Stat. 34, 97-104 (1986).

Let \(S(R^ n)\), E and \(\xi\) (\(\phi)\), \(\phi \in S(R^ n)\), be the same objects as in the review above (Zbl 0629.60056); the field \(\xi\) (\(\phi)\) is supposed to be homogeneous and isotropic in all variables. The paper gives necessary and sufficient conditions for the Markov property to hold for \(\xi\) (\(\phi)\). Markov property is understood in the Wong sense, i.e. “past” Hilbert space \(H(D_ 1)\) and the “future” Hilbert space \(H(D_ 2)\) are supposed to be uncorrelated for fixed “present” Hilbert space H(D), where \(D_ 1\), \(D_ 2\), D are mutually nested surfaces.

Reviewer: Yu.S.Mishura

MSC:

60G60	Random fields
60J25	Continuous-time Markov processes on general state spaces
46F99	Distributions, generalized functions, distribution spaces

Keywords:

random field; homogeneous and isotropic; Markov property

Citations:

Zbl 0629.60056