PhD thesis evaluation (Correlation in 2D Stochastic Equations Coupled Diffusively by Both Deterministic and Stochastic Components)

Activity

Internal examiner of PhD thesis

Description

In this thesis, my research focused on analyzing the interconnectedness of stochastic differential equations, examining the relationship between two variables in terms of their correlation, and exploring the concept of the pseudo-inverse Laplacian. Theoretical investigations were conducted to delve into the structural characteristics of SDEs, specifically determining methods to obtain their solutions.
I investigated synchronization phenomena by utilizing the generalized Langevin equation. I made novel discoveries regarding the application of the Laplacian matrix as a coefficient matrix in both the dynamic and stochastic components. This approach allowed me to observe correlations and simplify the correlation formula, leading to valuable insights in my research. Practical models of coupled Langevin equations were presented, and the impact of coefficients, particularly in the random component, on solution behavior and correlation values, was examined. Additionally, I introduced noisy components by employing the Laplacian matrix as the coefficient of the system. Moreover, I leveraged the properties of the pseudo-inverse Laplacian to derive a novel formula for determining the correlation of variables within the system.

Period	14 Mar 2025
Examinee	Wacharong Wongsanurak
Degree of Recognition	International