--- _id: '33331' abstract: - lang: eng 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. author: - first_name: Martin full_name: Kolb, Martin id: '48880' last_name: Kolb - first_name: Matthias full_name: Liesenfeld, Matthias last_name: Liesenfeld citation: ama: Kolb M, Liesenfeld M. Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems. Annales Henri Poincaré. 2019;20(6):1753-1783. doi:http://dx.doi.org/10.1007/s00023-019-00772-9 apa: Kolb, M., & Liesenfeld, M. (2019). Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems. Annales Henri Poincaré, 20(6), 1753–1783. http://dx.doi.org/10.1007/s00023-019-00772-9 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={http://dx.doi.org/10.1007/s00023-019-00772-9}, number={6}, journal={Annales Henri Poincaré}, publisher={Institute Henri Poincaré}, author={Kolb, Martin and Liesenfeld, Matthias}, year={2019}, pages={1753–1783} }' chicago: 'Kolb, Martin, and Matthias Liesenfeld. “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems.” Annales Henri Poincaré 20, no. 6 (2019): 1753–83. http://dx.doi.org/10.1007/s00023-019-00772-9.' ieee: 'M. Kolb and M. Liesenfeld, “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems,” Annales Henri Poincaré, vol. 20, no. 6, pp. 1753–1783, 2019, doi: http://dx.doi.org/10.1007/s00023-019-00772-9.' mla: Kolb, Martin, and Matthias Liesenfeld. “Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems.” Annales Henri Poincaré, vol. 20, no. 6, Institute Henri Poincaré, 2019, pp. 1753–83, doi:http://dx.doi.org/10.1007/s00023-019-00772-9. short: M. Kolb, M. Liesenfeld, Annales Henri Poincaré 20 (2019) 1753–1783. date_created: 2022-09-12T07:18:58Z date_updated: 2022-09-12T07:19:02Z department: - _id: '96' doi: http://dx.doi.org/10.1007/s00023-019-00772-9 intvolume: ' 20' issue: '6' language: - iso: eng page: 1753-1783 publication: Annales Henri Poincaré publication_status: published publisher: Institute Henri Poincaré status: public title: Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems type: journal_article user_id: '85821' volume: 20 year: '2019' ...