Estimates of Densities of Stationary Distributions and Transition Probabilities of Diffusion Processes

Bogachev VI, Röckner M, Shaposhnikov SV. Estimates of Densities of Stationary Distributions and Transition Probabilities of Diffusion Processes . Theory of Probability & Its Applications. 2008;52(2):209-236.We obtain lower bounds for solutions to second order elliptic and parabolic equations on the whole space. Our method is based on the study of the dependence of a constant in Harnack's inequality on the coefficients of the equation. As an application we obtain lower bounds for densities of stationary distributions and transition probabilities of diffusion processes with unbounded drift coefficients