The new stochastic integral and anticipating stochastic differential equations

Identifier

etd-06052012-150153

Author

Benedykt Szozda, Louisiana State University and Agricultural and Mechanical CollegeFollow

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

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.

Date

2012

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Recommended Citation

Szozda, Benedykt, "The new stochastic integral and anticipating stochastic differential equations" (2012). LSU Doctoral Dissertations. 1067.
https://repository.lsu.edu/gradschool_dissertations/1067

Committee Chair

Kuo, Hui-Hsiung

DOI

10.31390/gradschool_dissertations.1067