Total variation distance between SDEs with stable noise and Brownian motion

Abstract We consider d -dimensional stochastic differential equations (SDEs) of the form d upper U Subscript t Baseline equals b left parenthesis upper U Subscript t Baseline right parenthesis d t plus sigma d upper Z Subscript t Baseline d U t = b ( U t ) d t + σ d Z t $\textrm{d}U_t = b(U_t)\,\textrm{d}t + \sigma\,\textrm{d}Z_t$ . Let upper X Subscript t X t $X_t$ denote the solution if the driving noise upper Z Subscript t Z t $Z_t$ is a d -dimensional rotationally symmetric alpha α $\alpha$ -stable process ( 1 less than alpha less than 2 1 < α < 2 $1\lt \alpha\lt 2$ ), and let upper Y Subscript t Y t $Y_t$ be the solution if the driving noise is a d -dimensional Brownian motion. Continuing the work started in Deng et al. (2025), we derive an estimate of the total variation distance StartMetric law left parenthesis upper X Subscript t Baseline right parenthesis minus law left parenthesis upper Y Subscript t Baseline right parenthesis EndMetric Subscript TV ‖ law (