Search results for " 91A50"

showing 3 items of 3 documents

Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities

2018

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\Omega\subset \mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\Omega\times \Omega$ via couplings.

osittaisdifferentiaaliyhtälötPure mathematicsComputer Science::Computer Science and Game TheoryTug of war010102 general mathematicslocal Lipschitz estimatesLipschitz continuity01 natural sciencesnormalized p(x)-laplaciandynamic programming principle010104 statistics & probabilityMathematics - Analysis of PDEsFOS: Mathematicspeliteoria91A05 91A15 91A50 35B65 35J60 35J92stochastic games0101 mathematicsValue (mathematics)AnalysisAnalysis of PDEs (math.AP)Mathematicsstokastiset prosessit
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Hölder regularity for stochastic processes with bounded and measurable increments

2022

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.

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
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Local regularity estimates for general discrete dynamic programming equations

2022

We obtain an analytic proof for asymptotic H\"older estimate and Harnack's inequality for solutions to a discrete dynamic programming equation. The results also generalize to functions satisfying Pucci-type inequalities for discrete extremal operators. Thus the results cover a quite general class of equations.

local Hölder estimateosittaisdifferentiaaliyhtälötABP-estimateApplied MathematicsGeneral Mathematicsp-LaplacianMathematics::Analysis of PDEs35B65 35J15 35J92 91A50elliptic non-divergence form partial differential equation with bounded and measurable coefficientsdynamic programming principleMathematics - Analysis of PDEsHarnack's inequalitytug-of-war with noiseFOS: MathematicsPucci extremal operatorpeliteoriaepäyhtälötAnalysis of PDEs (math.AP)
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