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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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樓主
發(fā)表于 2025-3-21 17:28:56 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱(chēng)Notes on Tug-of-War Games and the p-Laplace Equation
編輯Mikko Parviainen
視頻videohttp://file.papertrans.cn/669/668264/668264.mp4
概述provides 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
叢書(shū)名稱(chēng)SpringerBriefs on PDEs and Data Science
圖書(shū)封面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
描述.This book addresses the interplay between stochastic processes and partial differential equations. More specifically, it focuses on the connection between the nonlinear p-Laplace equation and the stochastic game called tug-of-war with noise. The connection in this context was discovered approximately 15 years ago and has since provided new insights and approaches. These lecture notes provide a brief but detailed and accessible introduction to the subject and to the more research-oriented literature. The book also presents the parabolic case side by side with the elliptic case, highlighting the fact that elliptic and parabolic equations are close in spirit in certain aspects. Moreover, it covers some parts of the regularity theory for these problems.. .Graduate students and advanced undergraduate students with a basic understanding of probability and partial differential equations will find this book useful..
出版日期Book 2024
關(guān)鍵詞dynamic programming principle; equations in non-divergence form; normalized or game theoretic p-Laplac
版次1
doihttps://doi.org/10.1007/978-981-99-7879-3
isbn_softcover978-981-99-7878-6
isbn_ebook978-981-99-7879-3Series ISSN 2731-7595 Series E-ISSN 2731-7609
issn_series 2731-7595
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor
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沙發(fā)
發(fā)表于 2025-3-21 23:27:19 | 只看該作者
https://doi.org/10.1007/978-981-99-7879-3dynamic programming principle; equations in non-divergence form; normalized or game theoretic p-Laplac
板凳
發(fā)表于 2025-3-22 01:35:05 | 只看該作者
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
地板
發(fā)表于 2025-3-22 07:31:31 | 只看該作者
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.
5#
發(fā)表于 2025-3-22 10:49:15 | 只看該作者
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發(fā)表于 2025-3-22 14:36:45 | 只看該作者
Stochastic Tug-of-War Games,Next we start looking at the connection between stochastic processes and PDEs more closely.
7#
發(fā)表于 2025-3-22 19:50:40 | 只看該作者
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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發(fā)表于 2025-3-22 23:20:26 | 只看該作者
9#
發(fā)表于 2025-3-23 01:27:00 | 只看該作者
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.
10#
發(fā)表于 2025-3-23 07:59:04 | 只看該作者
Open Problems and Comments,In this section we state some open problems.
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