Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-07T14:25:30.719Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

Cattiaux, P. et al. (2009). Quasi-stationary distributions and diffusion models in population dynamics. Ann. Prob. 37, 1926–1926.Google Scholar
Collet, P., Martínez, S. and San Martín, J. (1995). Asymptotic laws for one-dimensional diffusions conditioned to nonabsorption. Ann. Prob. 23, 1300–1314.CrossRefGoogle Scholar
Ferrari, P. A., Martínez, S. and Picco, P. (1992). Existence of nontrivial quasi-stationary distributions in the birth-death chain. Adv. Appl. Prob. 24, 795–813.Google Scholar
Fukushima, M. (1980). Dirichlet Forms and Markov Processes (North-Holland Math. Library 23). North-Holland, Amsterdam.Google Scholar
Ikeda, N. and Watanabe, S. (1989). Stochastic Differential Equations and Diffusion Processes (North-Holland Math. Library 24), 2nd edn. North-Holland, Amsterdam.Google Scholar
Karlin, S. and Taylor, H. M. (1981). A Second Course in Stochastic Processes, 2nd edn. Academic Press, New York.Google Scholar
Kolb, M. and Steinsaltz, D. (2012). Quasi limiting behavior for one dimensional diffusions with killing. To appear in Ann. Prob. Google Scholar
Zettl, A. (2005). Sturm–Loiuville Theory (Math. Surveys Monogr. 121). American Mathematical Society, Providence, RI.Google Scholar