Andrew Allan: Catalogue data in Spring Semester 2021

Name Dr. Andrew Allan

401-4611-21LRough Path Theory Information 4 credits2VA. Allan, J. Teichmann
AbstractThe aim of this course is to provide an introduction to the theory of rough paths, with a particular focus on their integration theory and associated rough differential equations, and how the theory relates to and enhances the field of stochastic calculus.
ObjectiveOur first motivation will be to understand the limitations of classical notions of integration to handle paths of very low regularity, and to see how the rough integral succeeds where other notions fail. We will construct rough integrals and establish solutions of differential equations driven by rough paths, as well as the continuity of these objects with respect to the paths involved, and their consistency with stochastic integration and SDEs. Various applications and extensions of the theory will then be discussed.
Lecture notesLecture notes will be provided by the lecturer.
LiteratureP. K. Friz and M. Hairer, A course on rough paths with an introduction to regularity structures, Springer (2014).
P. K. Friz and N. B. Victoir. Multidimensional stochastic processes as rough paths, Cambridge University Press (2010).
Prerequisites / NoticeThe aim will be to make the course as self-contained as possible, but some knowledge of stochastic analysis is highly recommended. The course “Brownian Motion and Stochastic Calculus” would be ideal, but not strictly required.