Estimates of Densities of Stationary Distributions and Transition Probabilities of Diffusion Processes
Vladimir Igorevich Bogachev, Michael Röckner, Stanislav Valer'evich Shaposhnikov · Theory of Probability and Its Applications · 2008
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.