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Domain of attraction of quasi-stationary distributions for the brownian motion with drift

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Servet Martinez ,
Pierre Picco  and
Jaime San Martin
Servet Martinez*
Affiliation:
Universidad de Chile
Pierre Picco*
Affiliation:
CPT CNRS Luminy
Jaime San Martin*
Affiliation:
Universidad de Chile
*
∗ Postal address: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170, Correo3, Santiago 3, Chile.
∗∗ Postal address: CPT CNRS Luminy, Case 907, 13288, Marseille, Cedex 9, France.
∗ Postal address: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170, Correo3, Santiago 3, Chile.
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Abstract

We consider Brownian motion with a negative drift conditioned to stay positive. We give a sufficient condition for an initial measure to be in the domain of attraction of a quasi-stationary distribution. We construct a counter-example that strongly suggests that this condition is optimal.

Keywords

Quasi-stationary distributionsBrownian motion

MSC classification

Primary: 60J65: Brownian motion
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 2 , June 1998 , pp. 385 - 408
Copyright
Copyright © Applied Probability Trust 1998 

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