Hölder regularity for stochastic processes with bounded and measurable increments
Pablo Blanc
University of Jyväskylä, FinlandMikko Parviainen
University of Jyväskylä, FinlandÁngel Arroyo
Complutense University of Madrid, Spain

Abstract
We obtain an asymptotic Hölder estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, is a counterpart to the Krylov–Safonov regularity result in PDEs. However, the discrete step size ε has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments.
Cite this article
Pablo Blanc, Mikko Parviainen, Ángel Arroyo, Hölder regularity for stochastic processes with bounded and measurable increments. Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 1, pp. 215–258
DOI 10.4171/AIHPC/41