Numerical integration of stochastic contact Hamiltonian systems via stochastic Herglotz variational principle

In this work we construct a stochastic contact variational integrator and its discrete version via stochastic Herglotz variational principle for stochastic contact Hamiltonian systems. A general structure-preserving stochastic contact method is devised, and the stochastic contact variational integrators are established. The implementation of this approach is validated by the numerical experiments.