Search results for "tug-of-war with noise"

showing 3 items of 3 documents

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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Gradient and Lipschitz Estimates for Tug-of-War Type Games

2021

We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p$-harmonic function. Moreover, we establish an improved Lipschitz estimate when boundary values are close to a plane. Such estimates are known to play a key role in the higher regularity theory of partial differential equations. The proofs are based on cancellation and coupling methods as well as an improved version of the cylinder walk argument. peerReviewed

osittaisdifferentiaaliyhtälöt91A15 35B65 35J92gradient regularityApplied MathematicsTug of warMathematical analysisstochastic two player zero-sum gameType (model theory)Lipschitz continuityComputational MathematicsMathematics - Analysis of PDEsLipschitz estimateBellman equationtug-of-war with noiseFOS: MathematicsUniform boundednesspeliteoriaAlmost everywherep-LaplaceValue (mathematics)AnalysisAnalysis of PDEs (math.AP)Mathematicsstokastiset prosessit
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Regularity for nonlinear stochastic games

2015

We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed

viscosity solutionsDiscretization01 natural sciencesMathematics - Analysis of PDEsBellman equationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsApplied mathematicstug-of-war0101 mathematicsMathematics - Optimization and ControlMathematical PhysicsMathematicsstokastiset prosessitPartial differential equationApplied Mathematics91A15 35J92 35B65 35J60 49N60010102 general mathematicsta111dynamic programming principletug-of-war with noise with space dependent probabilities010101 applied mathematicsNonlinear systemOptimization and Control (math.OC)p-LaplaceAnalysisAnalysis of PDEs (math.AP)
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