[{"volume":40,"user_id":"85821","_id":"37503","publisher":"Institute of Mathematical Statistics","page":"162-212","status":"public","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>","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} }","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>.","short":"M. Kolb, D. Steinsaltz, Annals of Probability 40 (2012) 162–212.","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>."},"doi":"https://doi.org/10.1214/10-AOP623","language":[{"iso":"eng"}],"intvolume":"        40","publication_status":"published","date_updated":"2023-01-19T06:55:09Z","author":[{"first_name":"Martin","last_name":"Kolb","full_name":"Kolb, Martin","id":"48880"},{"full_name":"Steinsaltz, David","first_name":"David","last_name":"Steinsaltz"}],"title":"Quasilimiting behavior for one-dimensional diffusions with killing","year":"2012","department":[{"_id":"96"}],"type":"journal_article","date_created":"2023-01-19T06:55:03Z","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"}],"issue":"1","publication":"Annals of Probability"},{"citation":{"mla":"Grummt, Robert, and Martin Kolb. “Essential Selfadjointness of Singular Magnetic Schrödinger Operators on Riemannian Manifolds.” <i> Journal of Mathematical Analysis and Applications</i>, vol. 388, 2012, pp. 480–89, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2011.09.060\">10.1016/j.jmaa.2011.09.060</a>.","ama":"Grummt R, Kolb M. Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds. <i> Journal of Mathematical Analysis and Applications</i>. 2012;388:480-489. doi:<a href=\"https://doi.org/10.1016/j.jmaa.2011.09.060\">10.1016/j.jmaa.2011.09.060</a>","bibtex":"@article{Grummt_Kolb_2012, title={Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds}, volume={388}, DOI={<a href=\"https://doi.org/10.1016/j.jmaa.2011.09.060\">10.1016/j.jmaa.2011.09.060</a>}, journal={ Journal of Mathematical Analysis and Applications}, author={Grummt, Robert and Kolb, Martin}, year={2012}, pages={480–489} }","apa":"Grummt, R., &#38; Kolb, M. (2012). Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds. <i> Journal of Mathematical Analysis and Applications</i>, <i>388</i>, 480–489. <a href=\"https://doi.org/10.1016/j.jmaa.2011.09.060\">https://doi.org/10.1016/j.jmaa.2011.09.060</a>","ieee":"R. Grummt and M. Kolb, “Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds,” <i> Journal of Mathematical Analysis and Applications</i>, vol. 388, pp. 480–489, 2012, doi: <a href=\"https://doi.org/10.1016/j.jmaa.2011.09.060\">10.1016/j.jmaa.2011.09.060</a>.","short":"R. Grummt, M. Kolb,  Journal of Mathematical Analysis and Applications 388 (2012) 480–489.","chicago":"Grummt, Robert, and Martin Kolb. “Essential Selfadjointness of Singular Magnetic Schrödinger Operators on Riemannian Manifolds.” <i> Journal of Mathematical Analysis and Applications</i> 388 (2012): 480–89. <a href=\"https://doi.org/10.1016/j.jmaa.2011.09.060\">https://doi.org/10.1016/j.jmaa.2011.09.060</a>."},"publication":" Journal of Mathematical Analysis and Applications","date_created":"2023-06-26T08:04:27Z","department":[{"_id":"96"}],"type":"journal_article","author":[{"full_name":"Grummt, Robert","last_name":"Grummt","first_name":"Robert"},{"id":"48880","first_name":"Martin","last_name":"Kolb","full_name":"Kolb, Martin"}],"status":"public","year":"2012","title":"Essential selfadjointness of singular magnetic Schrödinger operators on Riemannian manifolds","intvolume":"       388","date_updated":"2023-06-26T08:04:47Z","language":[{"iso":"eng"}],"_id":"45765","page":"480-489","volume":388,"doi":"10.1016/j.jmaa.2011.09.060","user_id":"14931"},{"abstract":[{"lang":"eng","text":"We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue."}],"citation":{"apa":"Bassi, A., Dürr, D., &#38; Kolb, M. (2009). ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS. <i>Reviews in Mathematical Physics</i>, <i>22</i>(1), 55–89. <a href=\"https://doi.org/10.1142/S0129055X10003886\">https://doi.org/10.1142/S0129055X10003886</a>","ieee":"A. Bassi, D. Dürr, and M. Kolb, “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS,” <i>Reviews in Mathematical Physics</i>, vol. 22, no. 1, pp. 55–89, 2009, doi: <a href=\"https://doi.org/10.1142/S0129055X10003886\">https://doi.org/10.1142/S0129055X10003886</a>.","chicago":"Bassi, Angelo, Detlef Dürr, and Martin Kolb. “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS.” <i>Reviews in Mathematical Physics</i> 22, no. 1 (2009): 55–89. <a href=\"https://doi.org/10.1142/S0129055X10003886\">https://doi.org/10.1142/S0129055X10003886</a>.","short":"A. Bassi, D. Dürr, M. Kolb, Reviews in Mathematical Physics 22 (2009) 55–89.","mla":"Bassi, Angelo, et al. “ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS.” <i>Reviews in Mathematical Physics</i>, vol. 22, no. 1, 2009, pp. 55–89, doi:<a href=\"https://doi.org/10.1142/S0129055X10003886\">https://doi.org/10.1142/S0129055X10003886</a>.","ama":"Bassi A, Dürr D, Kolb M. ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS. <i>Reviews in Mathematical Physics</i>. 2009;22(1):55-89. doi:<a href=\"https://doi.org/10.1142/S0129055X10003886\">https://doi.org/10.1142/S0129055X10003886</a>","bibtex":"@article{Bassi_Dürr_Kolb_2009, title={ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS}, volume={22}, DOI={<a href=\"https://doi.org/10.1142/S0129055X10003886\">https://doi.org/10.1142/S0129055X10003886</a>}, number={1}, journal={Reviews in Mathematical Physics}, author={Bassi, Angelo and Dürr, Detlef and Kolb, Martin}, year={2009}, pages={55–89} }"},"issue":"1","publication":"Reviews in Mathematical Physics","department":[{"_id":"96"}],"type":"journal_article","date_created":"2023-01-19T06:49:37Z","intvolume":"        22","publication_status":"published","date_updated":"2023-01-19T06:49:46Z","author":[{"last_name":"Bassi","first_name":"Angelo","full_name":"Bassi, Angelo"},{"last_name":"Dürr","first_name":"Detlef","full_name":"Dürr, Detlef"},{"last_name":"Kolb","first_name":"Martin","full_name":"Kolb, Martin","id":"48880"}],"status":"public","title":"ON THE LONG TIME BEHAVIOR OF FREE STOCHASTIC SCHRÖDINGER EVOLUTIONS","year":"2009","volume":22,"user_id":"85821","doi":"https://doi.org/10.1142/S0129055X10003886","language":[{"iso":"eng"}],"_id":"37500","page":"55-89"}]