White Noise Methods for Anticipating Stochastic Differential Equations

White Noise Methods for Anticipating Stochastic Differential Equations

Doctor of Philosophy (Ph.D.)
Keywords :White Noise,Anticipating,Stochastic Differential Equations

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AbstractThis 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 Hitsuda-Skorokhod integral which nicely extends the It integral to anticipating integrands, we then apply the S-transform from white noise analysis to study this new equation.