College of Computer Science and Mathematics

Discussion of a master’s thesis in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

   “Using stratonovic integral formula for solving stochastic differential equations with application ”

In continuation of the scientific research movement and with the follow-up and presence of the Dean of the College of Computer Science and Mathematics

   Prof. Dr. Duha Bashir Abdullah The esteemed

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Monday 25-3-2024

Master’s thesis by student  Ibrahim Mohamed Mohideen Mohamed

 , under

the supervision of  Professor Dr. Abdulghafoor Jassim Salim.

This thesis included an introduction to stochastic differential equations and finding analytical solutions for them. In the event that the equations were non-linear, a method of transformations (reduction) was used to convert them to the linear form. Before starting most of the transformations, it was confirmed that the non-linear stochastic differential equations are reducible to linear stochastic differential equations using some special theories in this field. The Stratonowic integral formula was adopted to help in finding the solution and compared with the transformation methods using Ito’s integral formula so that the analytical solution can be found in a correct manner. Exactly.

The thesis also included numerical methods represented by the Euler-Maruyama and Milstein methods in order to compare with the solutions obtained by reduction or transformation methods. We also studied the convergence of the analytical solutions obtained from the Ito-Stratonovic formulas and the numerical methods. The absolute error, strong convergence, and weak convergence of the two numerical methods were also studied and presented.

It also included a study of the stability of the solution to linear and non-linear stochastic differential equations after finding the solutions using the Stratonovic integral formula using the second direct method of the scientist Lyapunov and the theories of stability and comparison of stability by finding the solution using the Ito integral formula.

The scientific committee included the following members :

• Professor Dr. Maysoon Malallah Aziiz – Chairman
• Assistant Professor Dr. Thaer Yunis Thenon – Member.
• Assistant Professor Dr. Ahmad Mohamed Jumah – Member .
• Professor Dr. Abdulghafoor Jassim Salim – Member and supervisor .