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Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process

Part of: Markov processes Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  14 July 2016

Manuel Lladser  and
Jaime San Martín
Manuel Lladser*
Affiliation:
Universidad de Chile
Jaime San Martín*
Affiliation:
Universidad de Chile
*
∗Postal address: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170, Correo 3, Santiago 3, Chile
∗Postal address: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170, Correo 3, Santiago 3, Chile
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Abstract

Let (Xt) be a one-dimensional Ornstein-Uhlenbeck process with initial density function f : ℝ+ → ℝ+, which is a regularly varying function with exponent -(1 + η), η ∊ (0,1). We prove the existence of a probability measure ν with a Lebesgue density, depending on η, such that for every A ∊ B(R+):

Keywords

Quasi-stationaryOrnstein-Uhlenbeck

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 60B10: Convergence of probability measures
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 511 - 520
Copyright
Copyright © by the Applied Probability Trust 2000 

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