Hölder regularity for stochastic processes with bounded and measurable increments
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.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
European Mathematical Society - EMS - Publishing House GmbH
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202303132128Use this for linking
Review status
Peer reviewed
ISSN
0294-1449
DOI
https://doi.org/10.4171/aihpc/41
Language
English
Published in
Annales de l’Institut Henri Poincaré : Analyse Non Linéaire
Citation
- Arroyo, Á., Blanc, P., & Parviainen, M. (2023). Hölder regularity for stochastic processes with bounded and measurable increments. Annales de l’Institut Henri Poincaré : Analyse Non Linéaire, 40(1), 215-258. https://doi.org/10.4171/aihpc/41
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
A. 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.
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