Comparison theorems for diffusion processes (Q919718)

The author proves an identity involving transition probabilities of two diffusion processes on \({\mathbb{R}}^ d\). From these comparison theorems he derives lower and upper bounds for the transition probabilities of a given diffusion process. The basic conditions are uniform ellipticity for the elliptic operator and uniform continuity of the coefficients. In contrast to the known estimates for fundamental solutions of parabolic equations the author's bounds do not depend on the moduli of continuity of the coefficients of the differential operator.