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 -correlated, i.e. the values are not correlated excluding an -neighbourhood of each point. The asymptotic expansions are derived for . 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.
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J. vom Scheidt, H.-J. Starkloff, R. Wunderlich, Asymptotic Expansions of Integral Functionals of Weakly Correlated Random Processes. Z. Anal. Anwend. 19 (2000), no. 1, pp. 255–268DOI 10.4171/ZAA/949