Volume 26, 2020
|Number of page(s)||31|
|Published online||10 December 2020|
Asymptotic Hölder regularity for the ellipsoid process
Department of Mathematics, University of Genoa,
Via Dodecaneso 35,
2 Department of Mathematics and Statistics, University of Jyväskylä, PO Box 35, 40014 Jyväskylä, Finland.
* Corresponding author: firstname.lastname@example.org
Accepted: 20 May 2020
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.
Mathematics Subject Classification: 35B65 / 35J15 / 60H30 / 60J10 / 91A50
Key words: Dynamic programming principle / local Hölder estimates / stochastic games / coupling of stochastic processes / ellipsoid process / equations in non-divergence form
© EDP Sciences, SMAI 2020
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