Weak approximation of reflected stochastic differential equations and sampling from distributions with compact support

This talk will be given by Michael Tretyakov (University of Nottingham)

Abstract: A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It is proved that the method converges with the first order.

Together with the Monte Carlo technique, it can be used to numerically solve linear parabolic and elliptic PDEs with Robin boundary condition. It is shown how the proposed method can be exploited for approximately computing expectations with respect to the invariant law of RSDEs, both inside a domain and on its boundary.

This allows to efficiently sample from distributions with compact support.

Both time-averaging and ensemble-averaging estimators are introduced and analysed. A number of extensions are considered, including a second-order weak approximation, the case of arbitrary oblique direction of reflection, and a new adaptive weak scheme to solve a Poisson PDE with Neumann boundary condition.

The presented theoretical results are supported by several numerical experiments. The talk is based on a joint work with Ben Leimkuhler (Edinburgh) and Akash Sharma (Nottingham).