Rare Events in the Stochastic Camassa–holm Equation

Abstract

We investigate rare or small probability events in the context of large deviations of the stochastic Camassa–Holm equation. By the weak convergence approach and regularization, we get large deviations of the regularized equation. Then, by stochastic equations exponentially equivalent to the corresponding laws, we get large deviations of the stochastic Camassa–Holm equation.