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Introduction to Random Tug-of-War Games and PDEs

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Book cover Regularity Estimates for Nonlinear Elliptic and Parabolic Problems

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 2045))

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Abstract

The fundamental contributions of Kolmogorov, Ito, Kakutani, Doob, Hunt, Lévy, and many others have shown the profound and powerful connection between classical linear potential theory and probability theory. The idea behind the classical interplay is that harmonic functions and martingales share a common cancelation property that can be expressed by using mean value properties. In these lectures, we will see how this approach turns out to very useful in the nonlinear theory as well.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    Juan J. Manfredi

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  1. Juan J. Manfredi
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Correspondence to Juan J. Manfredi .

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Manfredi, J.J. (2012). Introduction to Random Tug-of-War Games and PDEs. In: Regularity Estimates for Nonlinear Elliptic and Parabolic Problems. Lecture Notes in Mathematics(), vol 2045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27145-8_3

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