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October 1997 Asymptotics for the principal eigenvalue and eigenfunction of a nearly first-order operator with large potential
Wendell H. Fleming, Shuenn-Jyi Sheu
Ann. Probab. 25(4): 1953-1994 (October 1997). DOI: 10.1214/aop/1023481117

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.

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Wendell H. Fleming. Shuenn-Jyi Sheu. "Asymptotics for the principal eigenvalue and eigenfunction of a nearly first-order operator with large potential." Ann. Probab. 25 (4) 1953 - 1994, October 1997. https://doi.org/10.1214/aop/1023481117

Information

Published: October 1997
First available in Project Euclid: 7 June 2002

zbMATH: 0901.60033
MathSciNet: MR1487442
Digital Object Identifier: 10.1214/aop/1023481117

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

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.25 • No. 4 • October 1997
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