College of Computer Science and Mathematics

Discussion of Ph.D. Dissertation  in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“ The Stability and The Solutions (Analytic and reducibility) by Stratonovich – Formula for some Non-linear Stochastic Differential Equations with Application ”

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Thursday, 24 -6-2025.

Ph.D. Dissertation by Student Ali Mahmood Jumah Mohammed

under the supervision of Prof. Dr. Dr. Abdulghafoor Jasim Salim

The thesis addresses the analytical solutions of stochastic differential equations using the Ito-Stratonovich formula to find the stochastic integral. This is achieved by generalizing the theorems of the Ito- formula to the Stratonovich formula.

The stability of these solutions was also studied using the direct Lyapunov method using a system of stochastic differential equations. The moments of stochastic differential equations were also studied, utilizing the properties of the Wiener process.

This study was applied by constructing various models of stochastic differential equations on real data representing the number of cancer patients in Iraq for 1991-2023. The proposed models were represented by the stochastic quadratic model and the stochastic exponential model, and the Ito-Stratonovich formulas were used for each model. The optimal model for the time series was determined, represented by the stochastic quadratic model in the Stratonovich formula. The number of cancer patients was also predicted using the optimal model for the future time series from 2024-2035.

The scientific committee included the following members:

• Dr. Maysoun Mal Allah Aziz
• Dr. Raad Awad Hamid
• Dr. Saad Fawzi Jassim.
• Dr. Walid Mohammed Fathi
• Prof. Dr. Thaer Younis Dhnoon.
• Dr. Abdulghafoor Jasim Salim – Member and supervisor.