Topics in rough stochastic differential equations

Summary

Rough stochastic differential equations (RSDEs) are differential equations driven by a Brownian motion and a rough path. A RSDE can arises when some components of the driving Brownian motion in a stochastic differential equation are observable (that is conditioned to be fixed and given). General existence and uniqueness results for RSDEs with regular coefficients have been obtained recently in the preprint Friz-Hocquet-Lê "Rough stochastic differential equations" 2021. This PhD project aims to explore further topics related to this new class of equations. Problems include (but not limited to) long time behavior, numerical approximations, rough stochastic Lotka-Volterra equations, rough stochastic McKean-Vlasov equations.

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.