## The Annals of Probability

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

#### Abstract

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

#### Article information

Source
Ann. Probab., Volume 25, Number 4 (1997), 1953-1994.

Dates
First available in Project Euclid: 7 June 2002

https://projecteuclid.org/euclid.aop/1023481117

Digital Object Identifier
doi:10.1214/aop/1023481117

Mathematical Reviews number (MathSciNet)
MR1487442

Zentralblatt MATH identifier
0901.60033

Subjects
Primary: Primary 60H30
Secondary: 93B36 93E20

#### Citation

Fleming, Wendell H.; Sheu, Shuenn-Jyi. Asymptotics for the principal eigenvalue and eigenfunction of a nearly first-order operator with large potential. Ann. Probab. 25 (1997), no. 4, 1953--1994. doi:10.1214/aop/1023481117. https://projecteuclid.org/euclid.aop/1023481117

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