Reflected Stochastic Differential Equations on a Time-Dependent Non-Smooth Domain

Abstract: In this thesis we prove existence and uniqueness for reflected stochastic differential equation on a specific non-smooth, time-dependent domain. The domain is the intersection of a finite number of smooth domains that are allowed to vary in time. The reflection is oblique to the domain and at the corners more than one direction of reflection is allowed. The time restrictions on the domain is firstly the existence of a semiconcave family of sets that are C¹;+ in time. Secondly that the distance function to the domain is in W¹;p. The first part of the proof is to construct of three kinds of test functions with desired properties. Using these test functions, existence is proved to the Skorokhod problem. Finally uniqueness is proved for the reflected stochastic differential equation.