Game Theory and Partial Differential Equations

✍ Scribed by Pablo Blanc; Julio Daniel Rossi

Publisher: De Gruyter
Year: 2019
Tongue: English
Leaves: 236
Series: De Gruyter Series in Nonlinear Analysis and Applications; 31
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book collects several results in this direction and puts them in an elementary perspective in a lucid and self-contained fashion.

The first book on the subject of game theory and partial differential equations
Written by one of the main experts in the area
Of interest to researchers and graduate students in partial differential equations and applications

✦ Table of Contents

Preface
Acknowledgment
Contents
1. Random walks and the Laplacian
2. A first glimpse of the Tug-of-War games
3. Tug-of-War with noise
4. Tug-of-War
5. Mixed boundary conditions and the obstacle problem
6. Maximal operators
7. Games for eigenvalues of the Hessian
8. Parabolic problems
9. Free boundary problems
A. Viscosity solutions
B. Probability theory
Bibliography
Notations
Index

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