Strong convergence order for slow-fast SDEs in Hölder norm

Jicheng Liu and Guiling Long

Statistics & Probability Letters, 2025, vol. 222, issue C

Abstract: In this paper, we first derive a criterion for strong convergence in Hölder norm by the Garsia–Rodemich–Rumsey’s lemma. Then we apply the criterion to a class of stochastic differential equations with slow and fast time-scales, and deduce the averaging principle in Hölder norm using the technique of Poisson equation. As a byproduct, the strong convergence in sup-norm can be obtained.

Keywords: Averaging principle; Slow-fast; Poisson equation; Hölder norm (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110398

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