MARKOV PROCESSES AND DIFFUSION EQUATIONS ON UNBOUNDED INTERVALS

Abstract

This paper deals with some Feller semigroups acting on a particular weighted function space on [0;+1[ whose generators are degenerate elliptic second order differential operators. We show that these semigroups are the transition semigroups associated with suitable Markov processes on [0;+1]. Furthermore, by means of a sequence of discrete-type positive operators we introduced in a previous paper, we evaluate the expected value and the variance of the random variables describing the position of the processes and we give an approximation formula (in the weak topology) of the distribution of the position of the processes at every time, provided the distribution of the initial position is given and possesses finite moment of order two.