Asymptotic order of the expected length of excursions for the processes with a Scale mixture of normal distribution

摘要

The paper treats of the asymptotic order of the expected mean length of excursions for some ellipsoidal processes with a scale mixture of normal (SMN) distribution when the level is sufficiently large, which is the limiting values of ratios of two functions. It is shown that the Abelian theorem for the Laplace transforms and the Lu27Hopitalu27s rule are useful to estimate the asymptotic order. A general condition to derive the true asymptotic order of the ratios is also discussed.