Gel’fand–Yaglom type equations for calculating fluctuations around instantons in stochastic systems

@article{Schorlepp2021GelfandYaglomTE,
  title={Gel’fand–Yaglom type equations for calculating fluctuations around instantons in stochastic systems},
  author={Timo Schorlepp and Tobias Grafke and Rainer Grauer},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={54}
}
In recent years, instanton calculus has successfully been employed to estimate tail probabilities of rare events in various stochastic dynamical systems. Without further corrections, however, these estimates can only capture the exponential scaling. In this paper, we derive a general, closed form expression for the leading prefactor contribution of the fluctuations around the instanton trajectory for the computation of probability density functions of general observables. The key technique is… Expand
1 Citations
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Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization problem. The approachExpand

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