Local regularity for time-dependent tug-of-war games with varying\n probabilities

2015/12/07 by Mikko Parviainen, Parviainen, Mikko, Eero Ruosteenoja +1 · 3 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1512.02066

openalex publication_date 2015/12/07 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We study local regularity properties of value functions of time-dependent\ntug-of-war games. For games with constant probabilities we get local Lipschitz\ncontinuity. For more general games with probabilities depending on space and\ntime we obtain H "older and Harnack estimates. The games have a connection to\nthe normalized p(x,t)-parabolic equation (n+p(x,t))u_t=\Δ u+(p(x,t)-2)\n\Δ_\∞^N u.\n

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• A game-theoretic approach to the parabolic normalized p-Laplacian obstacle problem
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