Hölder regularity for stochastic processes with bounded and measurable increments
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http://hdl.handle.net/10045/140137
Title: | Hölder regularity for stochastic processes with bounded and measurable increments |
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Authors: | Arroyo, Ángel | Blanc, Pablo | Parviainen, Mikko |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Dynamic programming principle | Local Hölder estimates | Stochastic process | Equations in nondivergence form | p-harmonious | p-Laplace | Tug-of-war games |
Issue Date: | 1-Jul-2022 |
Publisher: | EMS Press |
Citation: | Annales de l'Institut Henri Poincaré. Analyse non linéaire. 2023, 40: 215-258. https://doi.org/10.4171/aihpc/41 |
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. |
Sponsor: | Á. A. is partially supported by a UniGe starting grant “Curiosity driven” and grants MTM2017-85666-P, 2017 SGR 395. B. P. and M. P. are partially supported by the Academy of Finland project #298641. |
URI: | http://hdl.handle.net/10045/140137 |
ISSN: | 0294-1449 (Print) | 1873-1430 (Online) |
DOI: | 10.4171/aihpc/41 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © 2022 Association Publications de l’Institut Henri Poincaré. Published by EMS Press. This work is licensed under a CC BY 4.0 license |
Peer Review: | si |
Publisher version: | https://doi.org/10.4171/aihpc/41 |
Appears in Collections: | Personal Investigador sin Adscripción a Grupo INV - GAM - Artículos de Revistas |
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Arroyo_etal_2023_AnnInstHPoincareAnalNonLineaire.pdf | 412,64 kB | Adobe PDF | Open Preview | |
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