Matching the test function's spatial regularity to that of the singular drift (Lebesgue, Hölder or negative Besov) improves or preserves weak convergence rates for discretization of SDEs with stable noise.
Euler--Maruyama scheme for $\alpha$-stable SDE with distributional drift
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abstract
In this paper, we consider a class of stochastic differential equations driven by symmetric non-degenerate $\alpha$-stable processes (including cylindrical ones) with $\alpha \in (1,2)$. We first establish a quantitative estimate for the Euler scheme under bounded drift $b(x)$, with an explicit dependence on $ \| b \|_{L^\infty}$. Then we obtain the weak convergence rates for the case where the drift coefficient belongs to a Besov space of negative order.
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math.PR 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Weak error for SDEs with additive stable noise and singular drift: choose the test function in the same space as the drift!
Matching the test function's spatial regularity to that of the singular drift (Lebesgue, Hölder or negative Besov) improves or preserves weak convergence rates for discretization of SDEs with stable noise.