Asymptotics for the principal eigenvalue and eigenfunction of a nearly first-order operator with large potential

被引：21

作者：

Fleming, WH ^{[1
]}

Sheu, SJ

机构：

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[2] Acad Sinica, Inst Math, Taipei, Taiwan

来源：

ANNALS OF PROBABILITY | 1997年 / 25卷 / 04期

关键词：

diffusion processes with small noise; first eigenvalue and eigenfunction; discounted control problem; viscosity solution; large deviations; risk sensitive control;

D O I：

10.1214/aop/1023481117

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：

The asymptotic behaviors of the principal eigenvalue and the corresponding normalized eigenfunction of the operator G(epsilon) f = (epsilon/2)Delta f + g del f + (l/epsilon)f for Small epsilon are studied. Under some conditions, the first order expansions for them are obtained. Two applications to risk-sensitive control problems are also mentioned.

引用

页码：1953 / 1994

页数：42

共 46 条

[1]

BENSOUSSAN A, 1992, J REINE ANGEW MATH, V429, P125

[2] AN ERGODIC CONTROL PROBLEM ARISING FROM THE PRINCIPAL EIGENFUNCTION OF AN ELLIPTIC OPERATOR [J].