Asymptotic Expansions of Integral Functionals of Weakly Correlated Random Processes

Abstract

the paper asymptotic expansions for second-order moments of integral functionals of a family of random processes are considered. The random processes are assumed to be wide-sense stationary and $ϵ$-correlated, i.e. the values are not correlated excluding an $ϵ$-neighbourhood of each point. The asymptotic expansions are derived for $ϵ\to 0$. Using a special weak assumption there are found easier expansions as in the case of general weakly correlated random processes. Expansions are given for integral functionals of real-valued as well as of complex vector-valued processes.