Title page for ETD etd-07052011-203013

Type of Document Dissertation
Author Sae-Tang, Anuwat
Author's Email Address asaeta2@lsu.edu, anuwat1983@yahoo.com
URN etd-07052011-203013
Title A New Theory of Stochastic Integration
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Kuo, Hui-Hsiung Committee Chair
Adkins, William Committee Member
Davidson, Mark Committee Member
Litherland, Richard Committee Member
Sundar, Padmanabhan Committee Member
Tzanov, Martin Dean's Representative
  • new stochastic integrals
  • Ayed-Kuo integrals
  • near-martingales
Date of Defense 2011-06-16
Availability unrestricted
In this dissertation, we focus mainly on the further study of the new stochastic integral introduced by Ayed and Kuo in 2008. Several properties of this new stochastic integral are obtained. We first introduce the concept of near-martingale for non-adapted stochastic processes. This concept is a generalization of the martingale property for adapted stochastic processes in the It\^o theory. We prove a special case of It\^o isometry for the stochastic integral of certain instantly independent processes. We obtain some formulas for expressing a new stochastic integral in terms of It\^o integrals and Riemann integrals. Several generalized versions of It\^o's formula for the new stochastic integral obtained by Ayed and Kuo are given. We also provide some examples to illustrate the ideas.
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