Title page for ETD etd-06052012-150153

Type of Document Dissertation
Author Szozda, Benedykt
URN etd-06052012-150153
Title The new stochastic integral and anticipating stochastic differential equations
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Kuo, Hui-Hsiung Committee Chair
Litherland, Richard Committee Member
Sengupta, Ambar Committee Member
Shipman, Stephen Committee Member
Sundar, Padmanabhan Committee Member
Hill, Carter Dean's Representative
Keywords
  • stochastic integration
  • stochastic differential equations
  • Ito formula
  • Ito integral
  • anticipating stochastic integral
  • instantaneous independence
  • Brownian motion
  • instantly independent processes
Date of Defense 2012-03-26
Availability unrestricted
Abstract
In this work, we develop further the theory of stochastic integration

of adapted and instantly independent stochastic processes started by

Wided Ayed and Hui-Hsiung Kuo in [1,2]. We

provide a first counterpart to the Itô isometry that accounts for

both adapted and instantly independent processes. We also present

several Itô formulas for the new stochastic integral. Finally, we

apply the new Itô formula to solve a linear stochastic

differential equations with anticipating initial conditions.
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