Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Quasistationary distributions for one-dimensional diffusions with killing


Authors: David Steinsaltz and Steven N. Evans
Journal: Trans. Amer. Math. Soc. 359 (2007), 1285-1324
MSC (2000): Primary 60J60
Published electronically: October 24, 2006
MathSciNet review: 2262851
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We extend some results on the convergence of one-dimensional diffusions killed at the boundary, conditioned on extended survival, to the case of general killing on the interior. We show, under fairly general conditions, that a diffusion conditioned on long survival either runs off to infinity almost surely, or almost surely converges to a quasistationary distribution given by the lowest eigenfunction of the generator. In the absence of internal killing, only a sufficiently strong inward drift can keep the process close to the origin, to allow convergence in distribution. An alternative, that arises when general killing is allowed, is that the conditioned process is held near the origin by a high rate of killing near $ \infty$. We also extend, to the case of general killing, the standard result on convergence to a quasistationary distribution of a diffusion on a compact interval.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 60J60

Retrieve articles in all journals with MSC (2000): 60J60


Additional Information

David Steinsaltz
Affiliation: Department of Demography, University of California, 2232 Piedmont Ave., Berkeley, California 94720
Email: dstein@demog.berkeley.edu

Steven N. Evans
Affiliation: Department of Statistics #3860, Evans Hall 367, University of California, Berkeley, California 94720-3860
Email: evans@stat.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03980-8
PII: S 0002-9947(06)03980-8
Received by editor(s): May 19, 2004
Received by editor(s) in revised form: December 26, 2004
Published electronically: October 24, 2006
Additional Notes: The first author was supported by Grant K12-AG00981 from the National Institute on Aging. The second author was supported in part by Grants DMS-00-71468 and DMS-04-05778 from the National Science Foundation, and by the Miller Institute for Basic Research in Science.
Article copyright: © Copyright 2006 David Steinsaltz and Steven N. Evans