Asymptotic Hölder Regularity for the Ellipsoid Process

Ángel Arroyo; Mikko Parviainen

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arXiv · 1905.02037

Asymptotic Hölder Regularity for the Ellipsoid Process

Ángel Arroyo·Mikko Parviainen

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Abstract

We obtain an asymptotic Hölder estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a generalization of the random walk where the next step in the process is taken inside a given space dependent ellipsoid. This stochastic process is related to elliptic equations in non-divergence form with bounded and measurable coefficients, and the regularity estimate is stable as the step size of the process converges to zero. The proof, which requires certain control on the distortion and the measure of the ellipsoids but not continuity assumption, is based on the coupling method.

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BibTeX RIS

Ángel Arroyo, Mikko Parviainen. 2020-08-04. Asymptotic Hölder Regularity for the Ellipsoid Process. https://arxiv.org/abs/1905.02037

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