Asymptotic Expansions of Integral Functionals of Weakly Correlated Random Processes

J. vom Scheidt, H.-J. Starkloff and R. Wunderlich

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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