Titlebook: Notes on Tug-of-War Games and the p-Laplace Equation; Mikko Parviainen Book 2024 The Editor(s) (if applicable) and The Author(s), under ex

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legacy

https://doi.org/10.1007/978-981-99-7879-3dynamic programming principle; equations in non-divergence form; normalized or game theoretic p-Laplac

ULCER

Mikko Parviainenprovides a detailed and accessible introduction to the subject and to the more research-oriented literature.presents illustrative examples and images to help readers understand the key ideas.introduce

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Introduction,inear potential theory and the corresponding probability theory. The connection between harmonic functions, the mean value property, and the expected value of a random walk is further illustrated in the examples. Such a connection appears to require linearity, but the approach turns out to be useful in the nonlinear theory as well.

LAIR

小故事

Stochastic Tug-of-War Games,Next we start looking at the connection between stochastic processes and PDEs more closely.

allergy

Cancellation Method for Regularity of the Tug-of-War with Noise,In this section, we show that a value function for the tug-of-war with noise is (asymptotically) locally Lipschitz continuous.

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locus-ceruleus

Further Regularity Methods,We already saw the cancellation method in Chap. . for the asymptotic Lipschitz regularity of value functions. It is a nontrivial task to extend that method to a more general class of problems where the sharp cancellation used in the proof breaks down. In this section, we review some regularity methods applicable with more general assumptions.

惰性氣體

Open Problems and Comments,In this section we state some open problems.