Electronic Journal of Probability

Principal eigenvalue for Brownian motion on a bounded interval with degenerate instantaneous jumps

Iddo Ben-Ari

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.

Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 87, 13 pp.

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

https://projecteuclid.org/euclid.ejp/1465062409

Digital Object Identifier
doi:10.1214/EJP.v17-1791

Mathematical Reviews number (MathSciNet)
MR2988402

Zentralblatt MATH identifier
1256.35033

Subjects
Primary: 35P15: Estimation of eigenvalues, upper and lower bounds

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