Hölder regularity for stochastic processes with bounded and measurable increments
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
Date
2023Discipline
MatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)Copyright
© Association Publications de l'Institut Henri Poincaré Paris
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.
Publisher
European Mathematical Society - EMS - Publishing House GmbHISSN Search the Publication Forum
0294-1449Keywords
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https://converis.jyu.fi/converis/portal/detail/Publication/148889823
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Research Council of FinlandFunding program(s)
Academy Project, AoFAdditional 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.License
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