Convergence of a canonical expansion for normal fields

E. I. Ostrovskii

M. V. Lomonosov Moscow State University

Abstract: In the present study we consider a normal separable stochastic continuous field, and we prove the convergence of a Karhunen series with probability 1 for all parameter values. This leads in particular, to the nonrandomness of points of the discontinuity and values of the discontinuity. A criterion is presented for the convergence of the canonical expansion in a uniform norm.

UDC: 519.21

Received: 09.06.1970

 English version: Mathematical Notes, 1973, 14:4, 881–885

Bibliographic databases:

• 
•