Sampling from mixture distributions based on regime-switching diffusions

TL;DR

This paper introduces a novel sampling method using stochastic differential equations with state-dependent switching rates, demonstrating convergence and practical effectiveness for finite mixture distributions.

Contribution

It proposes a new Euler scheme for SDEwS that converges with order one and applies it to sampling from mixture distributions, supported by theoretical and numerical validation.

Findings

Euler scheme for SDEwS converges with order one in weak sense

Scheme converges in the ergodic limit

Numerical experiments confirm theoretical results

Abstract

It is proposed to use stochastic differential equations with state-dependent switching rates (SDEwS) for sampling from finite mixture distributions. An Euler scheme with constant time step for SDEwS is considered. It is shown that the scheme converges with order one in weak sense and also in the ergodic limit. Numerical experiments illustrate the use of SDEwS for sampling from mixture distributions and confirm the theoretical results.