---
_id: '37503'
abstract:
- lang: eng
  text: 'This paper extends and clarifies results of Steinsaltz and Evans [Trans.
    Amer. Math. Soc. 359 (2007) 1285–1234], which found conditions for convergence
    of a killed one-dimensional diffusion conditioned on survival, to a quasistationary
    distribution whose density is given by the principal eigenfunction of the generator.
    Under the assumption that the limit of the killing at infinity differs from the
    principal eigenvalue we prove that convergence to quasistationarity occurs if
    and only if the principal eigenfunction is integrable. When the killing at ∞ is
    larger than the principal eigenvalue, then the eigenfunction is always integrable.
    When the killing at ∞ is smaller, the eigenfunction is integrable only when the
    unkilled process is recurrent; otherwise, the process conditioned on survival
    converges to 0 density on any bounded interval. '
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: David
  full_name: Steinsaltz, David
  last_name: Steinsaltz
citation:
  ama: Kolb M, Steinsaltz D. Quasilimiting behavior for one-dimensional diffusions
    with killing. <i>Annals of Probability</i>. 2012;40(1):162-212. doi:<a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>
  apa: Kolb, M., &#38; Steinsaltz, D. (2012). Quasilimiting behavior for one-dimensional
    diffusions with killing. <i>Annals of Probability</i>, <i>40</i>(1), 162–212.
    <a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>
  bibtex: '@article{Kolb_Steinsaltz_2012, title={Quasilimiting behavior for one-dimensional
    diffusions with killing}, volume={40}, DOI={<a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>},
    number={1}, journal={Annals of Probability}, publisher={Institute of Mathematical
    Statistics}, author={Kolb, Martin and Steinsaltz, David}, year={2012}, pages={162–212}
    }'
  chicago: 'Kolb, Martin, and David Steinsaltz. “Quasilimiting Behavior for One-Dimensional
    Diffusions with Killing.” <i>Annals of Probability</i> 40, no. 1 (2012): 162–212.
    <a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>.'
  ieee: 'M. Kolb and D. Steinsaltz, “Quasilimiting behavior for one-dimensional diffusions
    with killing,” <i>Annals of Probability</i>, vol. 40, no. 1, pp. 162–212, 2012,
    doi: <a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>.'
  mla: Kolb, Martin, and David Steinsaltz. “Quasilimiting Behavior for One-Dimensional
    Diffusions with Killing.” <i>Annals of Probability</i>, vol. 40, no. 1, Institute
    of Mathematical Statistics, 2012, pp. 162–212, doi:<a href="https://doi.org/10.1214/10-AOP623">https://doi.org/10.1214/10-AOP623</a>.
  short: M. Kolb, D. Steinsaltz, Annals of Probability 40 (2012) 162–212.
date_created: 2023-01-19T06:55:03Z
date_updated: 2023-01-19T06:55:09Z
department:
- _id: '96'
doi: https://doi.org/10.1214/10-AOP623
intvolume: '        40'
issue: '1'
language:
- iso: eng
page: 162-212
publication: Annals of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
status: public
title: Quasilimiting behavior for one-dimensional diffusions with killing
type: journal_article
user_id: '85821'
volume: 40
year: '2012'
...