Pathwise entropy solutions of SPDEs via rank-based models with common noise
Abstract
In this video, Mykhaylo Shkolnikov from Carnegie Mellon University delves into the emergence of pathwise entropy solutions for stochastic partial differential equations (SPDEs), pioneered by Gess and Souganidis, drawing on the groundwork laid by Lions, Perthame, and Souganidis. Exploring the intersection of stochastic portfolio theory and rank-based models, he unravels the probabilistic essence of pathwise entropy solutions, particularly under Brownian motion. This discussion is based on joint work with Lane Chun Yeung.
Watch recording ↗About the speaker
Professor of Mathematical Sciences, Professor Shkolnikov earned his PhD in Mathematics from Stanford University in 2012. Before joining Carnegie Mellon University, he was a tenured Associate Professor of Operations Research and Financial Engineering at Princeton University. Professor Shkolnikov was elected Fellow of the Institute of Mathematical Statistics in 2026. Professor Shkolnikov is the recipient of the 2018 Erlang Prize by the INFORMS Applied Probability Society and of the 2019 Early Career Prize by the SIAM Activity Group on Financial Mathematics & Engineering. He serves as an Associate Editor for Annals of Applied Probability, Applied Mathematical Finance, and Mathematical Finance. His research interests include stochastic portfolio theory, stochastic calculus, interacting particle systems, models of random growth, (stochastic) partial differential equations, and random matrices.