Estimates of the distribution of the maximum of discontinuous random fields. (Russian) Zbl 0696.60049

Mikushin, V. I.; Ostrovskij, E. I.

Teor. Veroyatn. Mat. Stat., Kiev 41, 50-56 (1989).

The article presents an exponential estimator of the probability \(P\{\) sup\(\{\) \(| \xi (t,s)|:\) (t,s)\(\in [0,1]^ 2\}>u\}\) for all \(u>1\) and a separable random field \(\xi\) under some positive sub-Gaussian property, improving earlier, known estimators. The proofs are based upon entropy estimators, known from works of G. Pisier, Yu. V. Kozachenko, X. Fernique.

Reviewer: E.I.Trofimov

MSC:

60G60

Random fields

Keywords:

random field; sub-Gaussian property; distribution of the paths maximum; exponential estimator; entropy estimators