Special Session 45: Frontiers in Topological Dynamics: Theory, Applications, and Interdisciplinary Connections

A Geometric Framework for Stochastic Dynamics on Manifolds of Probability Densities
Jinqiao Duan
Great Bay University
Peoples Rep of China
Co-Author(s):    
Abstract:
Traditional analysis of stochastic systems often relies on pathwise trajectories within Euclidean space. However, a more profound understanding of complex phenomena, such as critical transitions, emerges when these systems are viewed as evolutions on a manifold of probability densities. This talk explores this geometric perspective on the Onsager Machlup most probable paths, Schrodinger bridges, and information geodesics. This provides a cohesive framework that links calculus of variations and information geometry, offering new insights into the most probable behaviours of uncertain systems.