The significant advances in nonlinear stochastic dynamics and control in Hamiltonian formulation during the past decade are reviewed. The exact stationary solutions and equivalent nonlinear system method of Gaussian-white -noises excited and dissipated Hamiltonian systems, the stochastic averaging method for quasi Hamiltonian systems, the stochastic stability, stochastic bifurcation, first-passage time and nonlinear stochastic optimal control of quasi Hamiltonian systems are summarized. Possible extension and applications of the theory are pointed out. This review article cites 158 references.

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