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White noise methods for anticipating stochastic differential equations

This dissertation focuses on linear stochastic differential equations of anticipating type. Owing to the lack of a theory of differentiation for random processes, the said differential equations are appropriately understood and studied as anticipating stochastic integral equations. The unfolding work considers equations in which anticipation arises either from the initial condition or the integrand. In this regard, the techniques of white noise analysis are applied to such equations. In particular, by using the HitsudaSkorokhod integral which nicely extends the Itô integral to anticipating integrands, we then apply the S-transform from white noise analysis to study this new equation.