Roger Pettersson: Time-discetization for a stochastic Schrödinger equation with a time multipoint boundary condition

A Schrödinger equation driven by a cylindrical Brownian motion with a time multipoint boundary condition is considered. The initial value depends on a finite number of future values. Existence and uniqueness of a solution formulated as a mild solution is obtained. A single-step implicit Euler-Maruyama type difference scheme is suggested as a numerical solution. Convergence rate for the solution of the difference scheme is established. The theoretical statements for the difference scheme is supported by a numerical example. (Joint work with Ali Sirma and Tarkan Aydin).