An overall view of stochastics in Colombeau related algebras

Abstract

Stochastic analysis in Colombeau algebras was initiated by the works of Capar, Oberguggenberger and Russo in the early 1990s. The present communique is a comparative and critical account of the major research papers that have appeared so far in this particular field of study. It turns out that application of the nonlinear distribution theories of Colombeau and Rosinger to stochastic analysis provides new horizons in dealing with singular objects like nonlinear functions of white noise, Wiener functionals and nonlinear stochastic PDE, especially when the initial data is irregular or distributional.