Stochastic averaging of quasi partially integrable and resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitations

A stochastic averaging method for quasi partially integrable and resonant Hamiltonian systems excited by the combined Gaussian and Poisson white noises is proposed. The averaged stochastic integro-differential equations (SIDEs) and generalized Fokker-Planck-Kolmogorov (GFPK) equation for the quasi partially integrable Hamiltonian system with r(1