Weak error on the densities for the Euler scheme of stable additive SDEs with H{ö}lder drift

We are interested in the Euler-Maruyama dicretization of the SDE dXt =b(t,Xt)dt+ dZt, X0 =x$\in$Rd, where Zt is a symmetric isotropic d-dimensional $α$-stable process, $α$ $\in$ (1, 2] and the drift b $\in$ L$\infty$ ([0,T],C$β$(Rd,Rd)), $β$ $\in$ (0,1), is bounded and H{ö}lder regular in space. Using an Euler scheme with a randomization of the time variable, we show that, denoting $γ$,:= $α$ + $β$ – 1, the weak error on densities related to this discretization converges at the rate $γ$/$α$.

💡 Research Summary

This paper investigates the weak convergence of the Euler–Maruyama discretisation for stochastic differential equations (SDEs) driven by a symmetric isotropic α‑stable Lévy process in ℝ^d, with α∈(1,2]. The drift coefficient b(t,x) is assumed to be bounded in time (L^∞(