Weak convergence of diffusions corresponding to divergence form operators
Andrzej Rozkosz · Stochastics and stochastics reports · 1996
We construct diffusion measures corresponding to uniformly elliptic divergence form operators. Then we show that the measures converge weakly iff the associated operators G-converge in the sense defined by DeGiorgi and Spagnolo. As an application we characterize weak limit points of a tight sequence of diffusion measures with generators in divergent form and we find some connections between convergence of time-inhomogeneous and time-homogeneous diffusions. Some sufficient conditions for weak convergence of measures expressed in terms of coefficients of the corresponding generators are also given