Fluctuation theories and Gaussian stochastic processes

The theory of fluctuations for systems near equilibrium has given rise to two developments which generalize the theory in two distinct ways. One of these developments is focused on the theory of fluctuations far from equilibrium where the dynamics is nonlinear. The other development has focused on extending the class of fluctuating forces to include forces with non-delta function correlations. The near equilibrium theory corresponds with the theory of stationary, Gaussian, Markov processes; the nonlinear, far from equilibrium theory corresponds to the theory of nonstationary, Gaussian, Markov processes; and the non-delta function, force correlation theory corresponds to the theory of stationary, Gaussian, non-Markovian processes in one form, and to the theory of nonstationary, Gaussian, non-Markovian processes in another form. The common feature found in all these theories is Gaussianness.