Type of Document Dissertation Author Esunge, Julius URN etd-07062009-094329 Title White Noise Methods for Anticipating Stochastic Differential Equations Degree Doctor of Philosophy (Ph.D.) Department Mathematics Advisory Committee
Advisor Name Title Hui-Hsiung Kuo Committee Chair Ambar Sengupta Committee Member Padmanabhan Sundar Committee Member Robert Perlis Committee Member Stephen Shipman Committee Member Charles Monlezun Dean's Representative Keywords
- White Noise
- Stochastic Differential Equations
Date of Defense 2009-06-10 Availability unrestricted Abstract
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 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.
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