Some remarks on the transformation of filtered gaussian processes: a useful tool for stochastic analysis

This paper is aimed to briefly present the state of the art regarding the memoryless nonlinear transformations of filtered Gaussian processes. First, filtering a Gaussian white noise produces a Gaussian colored process. Secondly, applying a memoryless nonlinear transformation to the process obtained in the first step, this is mapped to a non-Gaussian process. Markov methods of stochastic dynamics are applicable to a limited number of classes of non-Gaussian processes: the previously obtained transformations allow one to use all Markov methods including Itô's stochastic calculus.