Extremes of a certain class of Gaussian processes
The paper investigates distribution of extremes of a Gaussian process. The considered task is formulated as asymptotic behaviour of the probability \(P \{\sup _{t\geq 0}(X(t)-ct^{\beta })>u \}\) when \(u\to +\infty \). The author derives such a kind of conclusions for zero mean Gaussian processes with variance function \(t^{2H}\) fulfilling some additional conditions and \(H<\beta \). The presented results cover fractional Brownian motion and locally stationary self-similar Gaussian processes.
scientific article; zbMATH DE number 1792540