Asymptotic Hölder regularity for the ellipsoid process

Arroyo, Ángel  ; Parviainen, Mikko

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 112.

Résumé

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.

Détail

DOI : 10.1051/cocv/2020034

Classification : 35B65, 35J15, 60H30, 60J10, 91A50
Keywords: Dynamic programming principle, local Hölder estimates, stochastic games, coupling of stochastic processes, ellipsoid process, equations in non-divergence form

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