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

TL;DR

This paper develops a structure-preserving stochastic integrator for contact Hamiltonian systems based on a stochastic Herglotz variational principle, validated through numerical experiments.

Contribution

It introduces a novel stochastic contact variational integrator derived from the stochastic Herglotz principle, enhancing numerical methods for stochastic contact Hamiltonian systems.

Findings

Successful construction of a stochastic contact variational integrator

Validation through numerical experiments demonstrating effectiveness

Preservation of geometric structure in stochastic systems

Abstract

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.