Weak approximation of Schrödinger–Föllmer diffusion

Abstract

We consider the weak convergence of the Euler–Maruyama approximation for Schrödinger–Föllmer diffusions, which are solutions of Schrödinger bridge problems and can be used for sampling from given distributions. We show that the distribution of the terminal random variable of the time-discretized process weakly converges to the target one under mild regularity conditions.