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)).