Conventional probabilistic analysis is performed based on a random variable concept. In nonlinear stochastic dynamics, the number of random variables to represent a random excitation becomes exponentially increased with the increase of duration, and consequently the stochastic computation confronts so-called curse-of-dimensionality. In this study first two types of variational formulation, convolution-type and exponential-type, are introduced to deal with stochastic dynamic systems specified with initial conditions, and those with initial-end conditions, respectively. The formulation opens a way to solve nonlinear dissipative stochastic problems using the variational approach. Next the random process based orthogonal expansion method is introduced to circumvent the curse-of-dimensionality, and the use of which in the variational formulation yields the discretized equations for computation.