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Uniqueness of Quasistationary Distributions and Discrete Spectra when ∞ is an Entrance Boundary and 0 is Singular

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  04 February 2016

Jorge Littin C.
Jorge Littin C.*
Affiliation:
Universidad de Chile
*
∗ Postal address: Departamento Ingeniería Matemática and Centro Modelamiento Matemático, UMR 2071 CNRS-UCHILE, Facultad Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile. Email address: jlittin@dim.uchile.cl
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Abstract

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We study quasistationary distributions on a drifted Brownian motion killed at 0, when +∞ is an entrance boundary and 0 is an exit boundary. We prove the existence of a unique quasistationary distribution and of the Yaglom limit.

Keywords

One-dimensional diffusionentrance boundaryquasistationary distributionexit boundary

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 60G99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 3 , September 2012 , pp. 719 - 730
Copyright
© Applied Probability Trust 

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