Since its introduction in the 1990s, the theory of rough paths has established itself as a powerful tool to analyze a variety of stochastic systems that are too “rough” for their solutions to exist in the class of functions that can be handled by classical analytical methods. The power of the theory resides in its ability to cleanly separate the probabilistic components from their purely analytic aspects. Among the early achievements of the theory have been various regularity estimates of the solutions to SDEs with respect to boundary conditions. Further results included analysis of solutions to SDEs driven by fractional Brownian motion for values of the Hurst parameter less than 1/2, good error estimates on the remainder in the stochastic Taylor expansion, a simpler proof and extension of the Freidlin-Wentzell large deviations, etc. More recently, the theory has seen an explosion of new results that caused its scope to expand considerably. For example, it has successfully been used to build efficient cubature methods on Wiener space with applications to numerical methods for solving the filtering problem and approximations of solutions of backward SDEs. Another recent development has been the combination of rough paths theory with Malliavin calculus to provide hypoellipticity results in non-Markovian situations. A completely different set of developments has been the successful application of some tailor-made variations of the theory to the solution of classes of stochastic PDEs.
This workshop will bring together experts in the theory of rough paths with researchers working in related areas of mathematics (probability, PDEs/SDEs, analysis, etc) and sciences in general. It will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.
(University of California, Los Angeles (UCLA))
Dan Crisan (Imperial College)
Peter Friz (Technische Universität Berlin and WIAS Berlin)
Massimiliano Gubinelli (Université de Paris IX (Paris-Dauphine))
Martin Hairer (University of Warwick)