{"title":"Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems","user_id":"85821","citation":{"bibtex":"@article{Kolb_Liesenfeld_2019, title={Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems}, volume={20}, DOI={<a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>}, number={6}, journal={Annales Henri Poincaré}, publisher={Institute Henri Poincaré}, author={Kolb, Martin and Liesenfeld, Matthias}, year={2019}, pages={1753–1783} }","ieee":"M. Kolb and M. Liesenfeld, “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems,” <i>Annales Henri Poincaré</i>, vol. 20, no. 6, pp. 1753–1783, 2019, doi: <a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>.","apa":"Kolb, M., &#38; Liesenfeld, M. (2019). Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems. <i>Annales Henri Poincaré</i>, <i>20</i>(6), 1753–1783. <a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>","chicago":"Kolb, Martin, and Matthias Liesenfeld. “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems.” <i>Annales Henri Poincaré</i> 20, no. 6 (2019): 1753–83. <a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>.","short":"M. Kolb, M. Liesenfeld, Annales Henri Poincaré 20 (2019) 1753–1783.","ama":"Kolb M, Liesenfeld M. Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems. <i>Annales Henri Poincaré</i>. 2019;20(6):1753-1783. doi:<a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>","mla":"Kolb, Martin, and Matthias Liesenfeld. “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems.” <i>Annales Henri Poincaré</i>, vol. 20, no. 6, Institute Henri Poincaré, 2019, pp. 1753–83, doi:<a href=\"http://dx.doi.org/10.1007/s00023-019-00772-9\">http://dx.doi.org/10.1007/s00023-019-00772-9</a>."},"_id":"33331","abstract":[{"text":"Motivated by the recent contribution (Bauer and Bernard in Annales Henri Poincaré 19:653–693, 2018), we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation. Problems of this type appear in the analysis of continuously monitored quantum systems. We extend the results of Bauer and Bernard (Annales Henri Poincaré 19:653–693, 2018) and prove a general result concerning the convergence to a homogeneous Poisson process using only classical probabilistic tools.","lang":"eng"}],"publisher":"Institute Henri Poincaré","issue":"6","doi":"http://dx.doi.org/10.1007/s00023-019-00772-9","intvolume":"        20","volume":20,"publication_status":"published","date_updated":"2022-09-12T07:19:02Z","author":[{"last_name":"Kolb","id":"48880","full_name":"Kolb, Martin","first_name":"Martin"},{"last_name":"Liesenfeld","first_name":"Matthias","full_name":"Liesenfeld, Matthias"}],"department":[{"_id":"96"}],"page":"1753-1783","language":[{"iso":"eng"}],"year":"2019","publication":"Annales Henri Poincaré","date_created":"2022-09-12T07:18:58Z","type":"journal_article","status":"public"}