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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 26, Fasc. 1,
pages 201 - 209
 

ON SEQUENCES OF THE WHITE NOISES

M. Beśka
Z. Ciesielski

Abstract: 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(X ), i where f is integrable with respect to the Gaussian noise and the random vectors X i 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).

2000 AMS Mathematics Subject Classification: Primary: 60H40; Secondary: 33C45, 42C10, 60F15, 60F20, 60F25.

Key words and phrases: Gebelein’s inequality, Hermite polynomials, Legendre polynomials, white noise, Wiener decomposition.

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