Zeitschrift für Analysis und ihre Anwendungen Vol. 19, No. 1, pp. 255268 (2000) 

Asymptotic Expansions of Integral Functionals of Weakly Correlated Random ProcessesJ. vom Scheidt, H.J. Starkloff and R. WunderlichUniv. Chemnitz, Fac. Math., D  09107 ChemnitzAbstract: In the paper asymptotic expansions for secondorder moments of integral functionals of a family of random processes are considered. The random processes are assumed to be widesense 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 realvalued as well as of complex vectorvalued processes. Keywords: asymptotic expansion, secondorder moment, random differential equation, weakly correlated process, stationary process, random vibration Classification (MSC2000): 60G12, 34F05, 41A60, 70L05 Full text of the article:
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