Asymptotic expansions of integral functionals of weakly correlated random processes (Q1978099)

Under suitable assumptions, the authors derive asymptotic expansions as \(\varepsilon\to 0\) of integral functionals of the form \(\int_I Q(s) {^\varepsilon f}(s)ds\), where \(Q\) is a real-valued deterministic function defined on an interval \(I\subset\mathbb{R}\) and, for any \(\varepsilon\to 0\), \(( {^\varepsilon f}(s))_{s\in I}\) is an \(\varepsilon\)-correlated wide-sense stationary random process which is either real or complex vector-valued. Two examples are given of differential equations with inhomogeneous terms containing \(f^\varepsilon\), whose solutions are of the form considered.