Title page for ETD etd-07062009-094329


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
  • Anticipating
  • 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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