A Baxter type theorem for a vector-valued Gaussian random field. (Russian) Zbl 0572.60038

Kurchenko, A. A.

Teor. Veroyatn. Mat. Stat. 30, 107-113 (1984).

The author continues his investigations of Baxter type theorems for vector-valued random fields as begun in ibid. 21, 86-97 (1979; Zbl 0412.60059). In the present paper such results are proved for vector- valued Gaussian random fields. The basic tool here is an exponential estimate of the tail probability for a quadratic form in independent random variables due to D. L. Hanson and F. T. Wright, Ann. Math. Stat. 42, 1079-1083 (1971; Zbl 0216.222).

Reviewer: M.Iosifescu

MSC:

60F15	Strong limit theorems
60G60	Random fields

Keywords:

vector-valued random fields; Gaussian random fields; exponential estimate of the tail probability

Citations:

Zbl 0412.60059; Zbl 0216.222