3. Transformations of random processes

A transformation of a random process is defined by the same function applied to any realization of the process, with the result Y(s _Y , ω) = f[X(s _X , ω)], where s _X and s _Y are the supports of X and Y respectively. The result of the transformation is itself a random process. In general, the function f can itself be random, for example in so-called "stochastic" algorithms. But in the context of this article, the function itself will be deterministic, which entails that the realization Y(s _Y , ω) is entirely determined by the realization X(s _X , ω). The function f may itself depend on the support, e.g. if s _...