INNOVATIVE STOCHASTIC FINITE DIFFERENCE METHODS IN MEAN FIELD GAMES: A WIENER PROCESS APPROACH

Abstract

This study explores the integration of Wiener processes into stochastic extensionsof mean field games (MFGs), employing nonstandard finite difference methods (NSFDMs)for enhanced accuracy and stability. We extend existing mathematical models in differential game theory, addressing the challenges of stochasticity and numerical approximation. Theresearch highlights the adaptability and precision of NSFDM in complex stochastic environ-ments, providing novel insights and methodologies for addressing planning issues in MFGs with Wiener processes.0Received