On the existence and uniqueness of diffusion processes with Wentzell's boundary conditions (Q1116185)

A diffusion process on a domain D in \(R^ d\) with smooth boundary \(\partial D\) is determined by a pair of analytical data (A,L), where A is a second order differential operator of elliptic type and L is Wentzell's boundary condition. The problem of constructing diffusion processes for given (A,L) is considered by using the notion of Poisson point processes of Brownian excursions and uniqueness of the solution of the stochastic differential equation is proved. It includes the unique existence of (A,L) diffusions in the case when the coefficient of the reflection may be degenerate.