---
_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'
...