Symplectic Integration Of Stochastic Hamiltonian Systems

This book provides an accessible overview concerning the stochastic numerical methods inheriting longtime dynamical behaviours of finite and infinitedimensional stochastic Hamiltonian systems. The longtime dynamical behaviours under study involve symplectic structure invariants ergodicity and invariant measure. The emphasis is placed on the systematic construction and the probabilistic superiority of stochastic symplectic methods which preserve the geometric structure of the stochastic flow o