Generalized strongly harmonizable random fields in normed spaces. (English. Russian original) Zbl 0738.60046

Ponomarenko, A. I.

Theory Probab. Math. Stat. 43, 143-151 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 43, 127-135 (1990).

Summary: Generalized harmonizable and strongly harmonizable random fields with values in normed spaces and defined on locally compact Abelian groups are considered. Studies are made of the connections between harmonizable fields and other classes of generalized fields in normed spaces, approximations of continuous fields by strongly harmonizable fields, and ergodic properties of harmonizable fields.

MSC:

60G60	Random fields
43A99	Abstract harmonic analysis
22B99	Locally compact abelian groups (LCA groups)
46G10	Vector-valued measures and integration
60G12	General second-order stochastic processes

Keywords:

strongly harmonizable random fields; locally compact Abelian groups; ergodic properties of harmonizable fields