A Generalized Ito Formula

Abstract

An Ito formula is developed in a context consistent with the development of abstract existence and unique- ness theorems for nonlinear stochastic partial differential equations, which are singular or degenerate. This is a generalization of an earlier Ito formula for Gelfand triples. After this, an existence theorem is presented for some singular and degenerate stochastic equations followed by a few examples.