The new stochastic integral and anticipating stochastic differential equations

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 It&ocirc isometry that accounts for both adapted and instantly independent processes. We also present several It&ocirc formulas for the new stochastic integral. Finally, we apply the new It&ocirc formula to solve a linear stochastic differential equations with anticipating initial conditions.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2012

Author dc:creator

• Szozda, Benedykt

• stochastic integration
• stochastic differential equations
• Ito formula
• Ito integral
• anticipating stochastic integral
• instantaneous independence
• Brownian motion
• instantly independent processes

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-06052012-150153
https://repository.lsu.edu/gradschool_dissertations/1067

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-2066