Journal of Applied Probability

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

Manuel Lladser and Jaime San Martín

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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 AB(R+): limt→∞ Pf(XtA | T0X > t) = ν(A).

Article information

Source
J. Appl. Probab. Volume 37, Number 2 (2000), 511-521.

Dates
First available in Project Euclid: 27 February 2002

Permanent link to this document
https://projecteuclid.org/euclid.jap/1014842554

Digital Object Identifier
doi:10.1239/jap/1014842554

Mathematical Reviews number (MathSciNet)
MR1781008

Zentralblatt MATH identifier
0963.60075

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60B10: Convergence of probability measures

Keywords
Quasi-stationary Ornstein-Uhlenbeck

Citation

Lladser, Manuel; San Martín, Jaime. Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process. J. Appl. Probab. 37 (2000), no. 2, 511--521. doi:10.1239/jap/1014842554. https://projecteuclid.org/euclid.jap/1014842554.


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