Hölder regularity for stochastic processes with bounded and measurable increments

2021/09/02 by Ángel Arroyo, Arroyo, Ángel, Pablo Blanc +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #35B65 #35J15 #60H30 #60J10 #91A50 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2109.01027

openalex publication_date 2021/09/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

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.

Cited by

• Tug-of-war games related to p-Laplace type equations with zeroth order terms

Related

• Local Hölder regularity for set-indexed processes
• Asymptotic Hölder Regularity for the Ellipsoid Process
• Local regularity estimates for general discrete dynamic programming equations
• Asymptotic C^1,γ-regularity for value functions to uniformly elliptic dynamic programming principles
• Discrete stochastic maximal regularity