6533b830fe1ef96bd1297c39

RESEARCH PRODUCT

Hölder regularity for stochastic processes with bounded and measurable increments

ÁNgel ArroyoPablo BlancMikko Parviainen

subject

todennäköisyyslaskentamatematiikkaApplied Mathematicsp-harmoniousProbability (math.PR)tug-of-war gamesstochastic processdynamic programming principlelocal Hölder estimatesFOS: Mathematicsequations in nondivergence formp-Laplace35B65 35J15 60H30 60J10 91A50Mathematical PhysicsAnalysisAnalysis of PDEs (math.AP)stokastiset prosessit

description

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 $\varepsilon$ has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments.

yearjournalcountryeditionlanguage
2022-07-01
http://urn.fi/URN:NBN:fi:jyu-202303132128