ESTIMATES OF DENSITIES OF STATIONARY DISTRIBUTIONS AND TRANSITION PROBABILITIES OF DIFFUSION PROCESSES

被引：16

作者：

Bogachev, V. I. ^{[1
]}

Roeckner, M. ^{[2
,3
]}

Shaposhnikov, S. V. ^{[1
]}

机构：

[1] MSU, Dept Math & Mech, Lab Probabil Theory, Moscow 119992, Russia

[2] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

[3] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2008年 / 52卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Harnack inequality; transition probabilities; stationary distribution; lower bounds for solutions to parabolic equations;

D O I：

10.1137/S0040585X97982967

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：209 / 236

页数：28

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