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Tug-of-War with Noise: Case p ∈ [2, ∞)

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A Course on Tug-of-War Games with Random Noise

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Abstract

This chapter introduces the Tug-of-War with random noise and establishes its relation to the p-Laplace equation in case p ≥ 2. The following topics are covered: the p-Laplacian and the p-harmonic functions, the mean value expansions and averaging principles, construction of Tug-of-War, dynamic programming principle, relation to Brownian motion when p = 2.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA

    Marta Lewicka

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  1. Marta Lewicka
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Lewicka, M. (2020). Tug-of-War with Noise: Case p ∈ [2, ∞). In: A Course on Tug-of-War Games with Random Noise. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-46209-3_3

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