Rates of convergence for multivariate SDEs driven by Lévy processes in the small-time stable domain of attraction

Abstract: This paper explores the rates of convergence of solutions for multivariate stochastic differential equations (SDEs) driven by L\'evy processes within the small-time stable domain of attraction (DoA). Explicit bounds are derived for the uniform Wasserstein distance between solutions of two L\'evy-driven SDEs, expressed in terms of driver characteristics. These bounds establish convergence rates in probability for drivers in the DoA, and yield uniform Wasserstein distance convergence for SDEs with additive noise. The methodology uses two couplings for L\'evy driver jump components, leading to sharp convergence rates tied to the processes' intrinsic properties.