Analytic semigroups and degenerate elliptic operators with unbounded coefficients: A probabilistic approach

By using techniques derived from the theory of stochastic differential equations, we prove that a class of second order degenerate elliptic operators having unbounded coefficients generates analytic semigroups in C-b(R-d), the space of uniformly continuous and bounded functions from R-d into R. (C) 2000 Academic Press.