Semigroups and diffusion processes
Brian Jefferies · Mathematical Proceedings of the Cambridge Philosophical Society · 1987
A basic problem of the theory of Markov processes is to find a semigroup S of operators on the bounded Borel measurable functions on ℝd, such that S is given by a transition function, andfor all f belonging to the domain of a given second-order elliptic differential operator D. A process is constructed from the transition function associated with S, and then one hopes to realize the process as one with continuous paths [2].