Asymptotic behavior of Lévy measure density corresponding to inverse local time

For a one dimensional diffusion process [D*.sub.s,m] and the harmonic transformed Process [mathematical expression not reproducible], the asymptotic behavior of the Levy measure density corresponding to the inverse local time at the regular end point is investigated. The asymptotic behavior of n*, the Levy measure density corresponding to [D*.sub.s,m], follows from asymptotic behavior of the speed measure m. However, that of [n.sup.h*], the Levy measure density corresponding to [mathematical expression not reproducible], is given by a simple form, n* multiplied by an exponential decay function, for any harmonic function h based on the original diffusion operator.