**Asymptotic Expansions for Second-Order Moments of
Integral Functionals of Weakly Correlated Random Functions **

*Jürgen vom Scheidt, Hans-Jörg Starkloff and Ralf Wunderlich*

Preprint 97-17, TU Chemnitz, Faculty of Mathematics

**Abstract :**

In the paper asymptotic expansions for second-order moments of
integral functionals of a class of random functions are considered.
The random functions are assumed to be $\eps$-correlated, i.e.\ the values
are not correlated excluding a $\eps$-neighbourhood of each point.
The asymptotic expansions are derived for $\eps\to 0$.
With the help of a special weak assumption
there are found easier expansions as in the case of general
weakly correlated functions (see vom Scheidt, J.: Stochastic Equations
of Mathematical Physics. Akademie-Verlag, Berlin (1990)).