ON SOME DIFFUSION PROCESSES WITH STATIONARY DISTRIBUTIONS

被引：6
作者：
Noarov, A. I. [1 ]
机构：
[1] RAS, Inst Computat Math, Moscow 119991, Russia
来源：
THEORY OF PROBABILITY AND ITS APPLICATIONS | 2010年 / 54卷 / 03期
关键词：
Fokker-Planck equation; diffusion process; invariant measure; SOLVABILITY;
D O I：
10.1137/S0040585X97984383
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：
This paper provides a sufficient condition (on the vector field f(x)), under which the stationary Fokker-Planck equation Delta u - div (uf) = 0 has a solution in the form of probability density. The stochastic differential equation with the drift f(x) has an invariant probabilistic measure under this condition. This condition is satisfied by some vector fields f (drifts) having a sequence of fixed locally stable points, which tends to infinity. Sometimes the proposed method turns out to be more effective than previously known methods based on the Lyapunov function.
引用
收藏
页码：525 / 533
页数：9
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