Mean exit time and escape probability for dynamical systems driven by Lévy noises (Q2878935)

The authors consider the problem of the approximate determination of the mean first exit time and escape probability for dynamic systems described by a stochastic differential equation with \(\alpha\)-stable type Lévy motions \(L^\alpha_t\).NEWLINENEWLINEThey propose a numerical algorithm for solving a deterministic integral-differential equation corresponding to the original stochastic differential equation. The algorithm is applied to an example for which the analytical and asymptotic solution are known. Both the analytical and numerical results show that the mean exit time depends strongly on the domain size and the value of the parameter \(\alpha\) in the \(L^\alpha_t\) process.