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arXiv · 1804.09501

Stochastic spikes and Poisson Approximation of one-dimensional stochastic differential equations with applications to continuously measured Quantum Systems

Martin Kolb·Matthias Liesenfeld
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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.

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Martin Kolb, Matthias Liesenfeld. 2018-04-25. Stochastic spikes and Poisson Approximation of one-dimensional stochastic differential equations with applications to continuously measured Quantum Systems. https://doi.org/10.1007/s00023-019-00772-9

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