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2012 Principal eigenvalue for Brownian motion on a bounded interval with degenerate instantaneous jumps
Iddo Ben-Ari
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Electron. J. Probab. 17: 1-13 (2012). DOI: 10.1214/EJP.v17-1791

Abstract

We consider a model of Brownian motion on a bounded open interval with instantaneous jumps. The jumps occur at a spatially dependent rate given by a positive parameter times a continuous function positive on the interval and vanishing on its boundary. At each jump event the process is redistributed uniformly in the interval. We obtain sharp asymptotic bounds on the principal eigenvalue for the generator of the process as the parameter tends to infinity. Our work answers a question posed by Arcusin and Pinsky.

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Iddo Ben-Ari. "Principal eigenvalue for Brownian motion on a bounded interval with degenerate instantaneous jumps." Electron. J. Probab. 17 1 - 13, 2012. https://doi.org/10.1214/EJP.v17-1791

Information

Accepted: 4 October 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1256.35033
MathSciNet: MR2988402
Digital Object Identifier: 10.1214/EJP.v17-1791

Subjects:
Primary: 35P15
Secondary: 60J65

JOURNAL ARTICLE
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Vol.17 • 2012
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