Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations

Lee, 1966, Comparison of closure approximation theories in turbulent mixing, Physics Fluids, 9, 363, 10.1063/1.1761680

Beran, 1968

Crandall, 1980, Non-Gaussian closure for random vibration of non-linear oscillators, Int. J. Non-Linear Mechanics, 15, 303, 10.1016/0020-7462(80)90015-3

Ariaratnam, 1980, Bifurcation in non-linear stochastic systems, 470

Assaf, 1976, Approximate analysis of non-linear stochastic systems, Int. J. Control., 23, 477, 10.1080/00207177608922174

Crandall, 1979, Heuristic and equivalent linearization techniques for random vibration of non-linear oscillators, Vol. 1, 211

Kraichnan, 1961, Dynamics of non-linear stochastic systems, J. math. Phys., 2, 124, 10.1063/1.1724206

Stratonovich, 1963, Vol. 1

Kramers, 1940, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica, 7, 284, 10.1016/S0031-8914(40)90098-2

Gradshteyn, 1981

1972

Itô, 1951, On stochastic differential equations, Mem. Am. math. Soc., 4, 51

Doob, 1953

Ito, 1951, On a formula concerning stochastic differentials, Nagoya math. J., 3, 55, 10.1017/S0027763000012216

Gear, 1971

Khaz'minskii, 1966, A limit theorem for the solution of differential equations with random right hand sides, Theory Probab. Applic., 11, 390, 10.1137/1111038

Davis, 1962

Dimentberg, 1982, An exact solution to a certain non-linear random vibration problem, Int. J. Non-linear Mechanics, 17, 231, 10.1016/0020-7462(82)90023-3