no. 1
Hölder regularity for stochastic processes with bounded and measurable increments
Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 1, pp. 215-258
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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.

Accepté le :
Publié le :
DOI : 10.4171/aihpc/41
Classification : 35J15, 60H30, 60J10, 91A50, 35B65
Keywords: dynamic programming principle, local Hölder estimates, stochastic process, equations in nondivergence form, p-harmonious, p-Laplace, tug-of-war games 
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     author = {Arroyo, \'Angel and Blanc, Pablo and Parviainen, Mikko},
     title = {H\"older regularity for stochastic processes with bounded and measurable increments},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {215--258},
     year = {2023},
     volume = {40},
     number = {1},
     doi = {10.4171/aihpc/41},
     language = {en},
     url = {https://www.numdam.org/articles/10.4171/aihpc/41/}
}
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Arroyo, Ángel; Blanc, Pablo; Parviainen, Mikko. Hölder regularity for stochastic processes with bounded and measurable increments. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 1, pp. 215-258. doi: 10.4171/aihpc/41

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