Stochastic Analysis and Applications 2025: In Honour of Terry Lyons

This book presents a selection of cutting-edge contributions from leading experts in the field, capturing the latest developments in stochastic analysis and its growing interface with neighboring disciplines. Stochastic analysis is a rapidly evolving branch of mathematics focused on the behavior of dynamical systems influenced by randomness. Over the past three decades, it has grown into one of the most vibrant and interdisciplinary areas of research, with profound impact on fields ranging from finance and physics to data science and engineering. Topics include rough path theory, stochastic control, stochastic partial differential equations, random matrices, and applications in machine learning. Building on the success of a recent international conference that brought together researchers from both academia and industry, this proceedings book highlights the depth and breadth of current work in the field. It serves as a valuable resource not only for academic researchers in mathematics, but also for practitioners working in areas such as quantitative finance, data-driven modeling, and applied probability.