Arroyo, Ángel, Blanc, Pablo, Parviainen, Mikko
Hölder regularity for stochastic processes with bounded and measurable increments
Annales de l'Institut Henri Poincaré. Analyse non linéaire. 2023, 40: 215-258. https://doi.org/10.4171/aihpc/41
URI: http://hdl.handle.net/10045/140137
DOI: 10.4171/aihpc/41
ISSN: 0294-1449 (Print)
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.
Keywords:Dynamic programming principle, Local Hölder estimates, Stochastic process, Equations in nondivergence form, p-harmonious, p-Laplace, Tug-of-war games
EMS Press
info:eu-repo/semantics/article