Abstract :
We consider uniformly elliptic diffusion processes X(t,x) on Euclidean spaces Rd, with some conditions in terms of the drift term (see assumptions A2 and A3). By using interpolation theory, we show a bounded property which gives an estimate of ∇xE[ f(X(t,x))] involving |x| and || f||∞ but not ||∇f||∞, and a power of 1t smaller than 1.
