{"department":[{"_id":"96"}],"doi":"https://doi.org/10.1214/10-AOP623","publication_status":"published","volume":40,"issue":"1","author":[{"full_name":"Kolb, Martin","first_name":"Martin","last_name":"Kolb","id":"48880"},{"last_name":"Steinsaltz","first_name":"David","full_name":"Steinsaltz, David"}],"status":"public","page":"162-212","intvolume":"        40","type":"journal_article","user_id":"85821","title":"Quasilimiting behavior for one-dimensional diffusions with killing","date_updated":"2023-01-19T06:55:09Z","language":[{"iso":"eng"}],"abstract":[{"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. ","lang":"eng"}],"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>","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>.","short":"M. Kolb, D. Steinsaltz, Annals of Probability 40 (2012) 162–212.","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>.","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>.","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} }"},"year":"2012","_id":"37503","publication":"Annals of Probability","publisher":"Institute of Mathematical Statistics","date_created":"2023-01-19T06:55:03Z"}