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
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)).