Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems
M. Kolb, M. Liesenfeld, Annales Henri Poincaré 20 (2019) 1753–1783.
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Kolb, MartinLibreCat;
Liesenfeld, Matthias
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Abstract
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.
Publishing Year
Journal Title
Annales Henri Poincaré
Volume
20
Issue
6
Page
1753-1783
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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
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
@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} }
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.
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.
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.
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