Geodesic
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

Voir la notice de l'article provenant de la source Numdam

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 
@article{AIHPC_2023__40_1_215_0,
     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},
     volume = {40},
     number = {1},
     year = {2023},
     doi = {10.4171/aihpc/41},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/41/}
}
TY  - JOUR
AU  - Arroyo, Ángel
AU  - Blanc, Pablo
AU  - Parviainen, Mikko
TI  - Hölder regularity for stochastic processes with bounded and measurable increments
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2023
SP  - 215
EP  - 258
VL  - 40
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4171/aihpc/41/
DO  - 10.4171/aihpc/41
LA  - en
ID  - AIHPC_2023__40_1_215_0
ER  - 
%0 Journal Article
%A Arroyo, Ángel
%A Blanc, Pablo
%A Parviainen, Mikko
%T Hölder regularity for stochastic processes with bounded and measurable increments
%J Annales de l'I.H.P. Analyse non linéaire
%D 2023
%P 215-258
%V 40
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/aihpc/41/
%R 10.4171/aihpc/41
%G en
%F AIHPC_2023__40_1_215_0
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

Cité par Sources :