ASYMPTOTIC BEHAVIOUR OF THE INTEGRAL OF A FUNCTION ONTHE LEVEL SET OF A MIXING RANDOM FIELD
Abstract: Let be a centered stationary real random field with a.s.
differentiable paths. Let be a rectangle of and let denote the integral of the
continuous function over a level curve of for a fixed level observed in
We show that if a field satisfies some mixing condition, then
adequately normalized, converges weakly to the Wiener process indexed in 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 are finite.