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Zeitschrift für Analysis und ihre Anwendungen


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Volume 19, Issue 1, 2000, pp. 255–268
DOI: 10.4171/ZAA/949

Published online: 2000-03-31

Asymptotic Expansions of Integral Functionals of Weakly Correlated Random Processes

J. vom Scheidt[1], H.-J. Starkloff[2] and R. Wunderlich[3]

(1) Technische Universität Chemnitz, Germany
(2) Technische Universität Chemnitz, Germany
(3) Technische Universität Chemnitz, Germany

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 $\epsilon$-correlated, i.e. the values are not correlated excluding an $\epsilon$-neighbourhood of each point. The asymptotic expansions are derived for $\epsilon \to 0$. 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.

Keywords: Asymptotic expansion, second-order moment, random differential equation, weakly correlated process, stationary process, random vibration

vom Scheidt J., Starkloff H.-J., Wunderlich R.: Asymptotic Expansions of Integral Functionals of Weakly Correlated Random Processes. Z. Anal. Anwend. 19 (2000), 255-268. doi: 10.4171/ZAA/949