Estimates of densities of stationary distributions and transition probabilities of diffusion processes

V. I. Bogachev   ; M. Röckner   ; S. V. Shaposhnikov

Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 2, pp. 240-270

Résumé

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.

Détail

Keywords: Harnack inequality, transition probabilities, stationary distribution, lower bounds for solutions to parabolic equations.

Bibliographie

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