• Corpus ID: 119315679

Gumbel distribution in exit problems

@article{Bakhtin2013GumbelDI,
  title={Gumbel distribution in exit problems},
  author={Yuri Bakhtin},
  journal={arXiv: Probability},
  year={2013}
}
  • Yuri Bakhtin
  • Published 26 July 2013
  • Mathematics
  • arXiv: Probability
We explain the connection between the Gumbel limit for diffusion exit times and the theory of extreme values. 
View PDF on arXiv
6 Citations
Highly Influential Citations
2
Background Citations
3
Methods Citations
2

6 Citations

Citation Type

Citation Type

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References

SHOWING 1-10 OF 23 REFERENCES
Noisy heteroclinic networks
We consider a white noise perturbation of dynamics in the neighborhood of a heteroclinic network. We show that under the logarithmic time rescaling the diffusion converges in distribution in a…
Conditional Exits for Small Noise Diffusions with Characteristic Boundary
The small noise exit problem of Wentzell and Freidlin is of particular interest for regions whose boundary consists of trajectories of the underlying (unperturbed) dynamical system. This is called…
Small noise limit for diffusions near heteroclinic networks
This is a nontechnical exposition of the theory on vanishing noise limit for random perturbations of dynamical systems admitting heteroclinic networks developed by the author [Y. Bakhtin, Noisy…
ON THE EXIT LAW FROM SADDLE POINTS
Decision Making Times in Mean-Field Dynamic Ising Model
We consider a dynamic mean-field ferromagnetic model in the low-temperature regime in the neighborhood of the zero magnetization state. We study the random time it takes for the system to make a…
The Stochastic Process π
TLDR
This chapter familiarizes the reader with the fact that the conditional distribution of the signal can be viewed as a stochastic process with values in the space of probability measures.
Probability...
TLDR
This course can be used as a preparation for the first (Probability) actuarial exam and the central limit theorem and classical sampling distributions.
Convergence of probability measures
The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the…
On the Noise-Induced Passage through an Unstable Periodic Orbit II: General Case
TLDR
For a large class of such systems, the cycling profile is given, up to a model-dependent change of coordinates, by a universal function given by a periodicized Gumbel distribution.
Ann
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed…
...
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