Approximation by positive operators of the C0-semigroups associated with one-dimensional diffusion equations:: Part II

In this second part of the paper we state some general conditions that guarantee that the C-o-semigroups generated by special classes of one-dimensional second-order differential operators acting on weighted spaces of continuous functions on an arbitrary real interval can be represented as limits of iterates of the positive linear operators constructively defined according to the method developed in the first part. The particular case where the interval is compact is treated in full detail. Finally, an application to the Black-Scholes equation, which appears in some models arising from mathematical finance, is discussed as well.