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

摘要

In this paper we provide a proof of the conjecture for the asymptotic order of the expected mean length of excursions for some ellipsoidal processes with a scale mixture of normal (SMN) distribution whose mixing distribution is the generalized Gamma distribution, which was presented in the previous paper of Tanaka [15]. It is seen that the Lu27Hopitalu27s rule and the Abelian theorem for the two-sided Laplace transforms are useful to evaluate the asymptotic order in the proof.