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

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

Wendell H. Fleming and Shuenn-Jyi Sheu

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

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.

Primary Subjects: Primary 60H30

Secondary Subjects: 93B36, 93E20

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

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1023481117
Mathematical Reviews number (MathSciNet): MR1487442
Digital Object Identifier: doi:10.1214/aop/1023481117

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