Zeitschrift für Analysis und ihre Anwendungen
Vol. 19, No. 1, pp. 255-268 (2000)
Asymptotic Expansions of Integral Functionals of Weakly Correlated Random Processes
J. vom Scheidt, H.-J. Starkloff and R. WunderlichUniv. Chemnitz, Fac. Math., D -- 09107 Chemnitz
Abstract: In 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 $\e$-correlated, i.e. the values are not correlated excluding an $\e$-neighbourhood of each point. The asymptotic expansions are derived for $\e \to 0$. 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
Classification (MSC2000): 60G12, 34F05, 41A60, 70L05
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Electronic fulltext finalized on: 25 Jul 2001. This page was last modified: 9 Nov 2001.