Convergence analysis of the improved θ-scheme for two-dimensional double singular stochastic Volterra integral equations

This study contributes to the understanding of the behavior of two-dimensional double singular stochastic Volterra integral equations (DSSVIEs) and provides a comprehensive analysis of their properties. The evaluation of well-posedness, convergence, and the introduction of a numerical technique such as the improved ?-scheme (ITS) for solving the equation offer valuable insights for future research in this field. The proposed improvement utilizing sum-of-exponentials (SOE) approximation promises enhanced computational efficiency, which is crucial for practical applications. Overall, this study advances the knowledge of two-dimensional DSSVIEs and provides a solid foundation for further investigation and development in this area. An example is presented to demonstrate the effectiveness of the results achieved.