Stochastic spikes and Poisson Approximation of one-dimensional stochastic differential equations with applications to continuously measured Quantum Systems
Mathematical Physics
2019-06-26 v1 math.MP
Probability
Abstract
Motivated by the recent contribution \cite{BB17} 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 \cite{BB17} and prove a general result concerning the convergence to a homogeneous Poisson process using only classical probabilistic tools.
Keywords
Cite
@article{arxiv.1804.09501,
title = {Stochastic spikes and Poisson Approximation of one-dimensional stochastic differential equations with applications to continuously measured Quantum Systems},
author = {Martin Kolb and Matthias Liesenfeld},
journal= {arXiv preprint arXiv:1804.09501},
year = {2019}
}
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