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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 10, Fasc. 1,
pages 45 - 56
 

ASYMPTOTIC BEHAVIOUR OF THE INTEGRAL OF A FUNCTION ON THE LEVEL SET OF A MIXING RANDOM FIELD

Ileana Iribarren

Abstract: Let X = (X(t) : t  (-  R2) be a centered stationary real random field with a.s. differentiable paths. Let T be a rectangle of R2  and let F (f,T ) denote the integral of the continuous function f over a level curve C
 x  of X for a fixed level x, observed in T. We show that if a field X satisfies some mixing condition, then F(f,T), adequately normalized, converges weakly to the Wiener process indexed in T. The limit variance has a precise expression in the Gaussian case and *-mixing case. A geometrical lemma shows cases where the higher order moments of F (f,T ) are finite.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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