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On sequences of the white noises

Beśka M., Ciesielski Z.

Probability and Mathematical Statistics

2006

Vol. 26, Fasc. 1

201--209

The aim of the paper is to prove the strong law of large numbers for Gaussian functionals (Theorem 3.1). The functionals are of the form f (Xi), where / is integrable with respect to the Gaussian noise and the random vectors Xi are coordinatewise suitable correlated. In the last section we comment on the possibility of building noise analysis corresponding to the Legendre orthogonal polynomials analogous to the Wiener white noise theory based on Hermite orthogonal polynomials (Mehler’s kernel).