The excursions of a stationary Gaussian process outside a large two-dimensional region
The author studies a two-dimensional stationary Gaussian process \(X(t)= (X_1(t),X_2(t))\) with mean zero, covariance matrix \(R(T)\) and marginal density \(p(x).\) The asymptotic distribution of the duration of an excursion of \(X(t)\) outside star-shaped regions having a piecewise smooth boundary are studied. The asymptotic behaviour is found to depend on three cases determined by the position of the maximum of \(p(x)\) and the value of \(R'(0).\) Some generalizations of results on the asymptotic crossing rates are obtained.
scientific article; zbMATH DE number 1621397