Oscillatory Survival Probability: Analytical and Numerical Study of a Non-Poissonian Exit Time

@article{Duc2016OscillatorySP,
  title={Oscillatory Survival Probability: Analytical and Numerical Study of a Non-Poissonian Exit Time},
  author={Khanh Dao Duc and Zeev Schuss and David Holcman},
  journal={Multiscale Model. Simul.},
  year={2016},
  volume={14},
  pages={772-798}
}
We consider the escape of a planar diffusion process from the domain of attraction $\Omega$ of a stable focus of the drift in the limit of small diffusion. The boundary $\partial\Omega$ of $\Omega$ is an unstable limit cycle of the drift, and the focus is close to the limit cycle. A new phenomenon of oscillatory decay of the peaks of the survival probability of the process in $\Omega$ emerges for a specific distance of the focus to the boundary which depends on the amplitude of the diffusion… 

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