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Boundary Aware 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 improves on the construction of the Tug-of-War game in Chap. 3 and proves convergence of its values to p-harmonic functions, in the simplified nondegenerate case. This first convergence theorem is shown both via probabilistic and analytic techniques. Additionally, we continue discussing the relation to Brownian motion in case p = 2, begun in Chap. 3.

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Notes

  1. 1.

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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). Boundary Aware 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_4

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