The action functional for a class of stochastic processes

Let $x_t$ be a Gaussian process with zero mean and correlation operator $A$. The action functional for this process is defined by the equality $S(\varphi)=(A^{-1/2}\varphi,A^{-1/2}\varphi)$. We prove a number of theorems concerning action functionals which enable us to solve some asymptotic problems for Gaussian processes and processes obtained from Gaussian ones by nonlinear transforms.