ON INTEGRAL OF A SEMI-MARKOV DIFFUSION PROCESS

摘要

Let (X(t)) (t≥ 0) be a semi-Markov diffusion process. The process (J(T)) (T≥ 0) equal to the integral of (X(t)) on interval [0,T) is studied. The relation between one-dimensional differential equation of the second order of elliptical type and asymptotics of a solution to Dirichlet problem on an interval with length tending to zero is established. This relation is used to derive a differential equation for the Laplace transform of the semi-Markov generating function of the process (J(t)).