Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Quasistationary distributions for one-dimensional diffusions with killing
HTML articles powered by AMS MathViewer

by David Steinsaltz and Steven N. Evans PDF
Trans. Amer. Math. Soc. 359 (2007), 1285-1324


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.
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:
  • Steven N. Evans
  • Affiliation: Department of Statistics #3860, Evans Hall 367, University of California, Berkeley, California 94720-3860
  • MR Author ID: 64505
  • Email:
  • 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.
  • © Copyright 2006 David Steinsaltz and Steven N. Evans
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 1285-1324
  • MSC (2000): Primary 60J60
  • DOI:
  • MathSciNet review: 2262851