General Existence of Solutions to Dynamic Programming Principle

2013/07/07 by Qing Liu, Armin Schikorra, Liu, Qing +1
Economics, Econometrics and Finance · Mathematics · #35A35 #49C20 #91A05 #91A15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Biology Tumor Growth #Stochastic processes and financial applications #math.AP #msc:35A35 #msc:49C20 #msc:91A05 #msc:91A15

paper · pdf · doi:10.48550/arxiv.1307.1860

openalex publication_date 2013/07/07 · arxiv created 2013/07/18 · arxiv updated 2013/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an alternative approach to the existence of solutions to dynamic programming equations arising in the discrete game-theoretic interpretations for various nonlinear partial differential equations including the infinity Laplacian, mean curvature flow and Hamilton-Jacobi type. Our general result is similar to Perron's method but adapted to the discrete situation.

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