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Game Theory and Partial Differential Equations

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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.

Author(s): Pablo Blanc, Julio Daniel Rossi
Series: Series in Nonlinear Analysis and Applications 31
Publisher: De Gruyter
Year: 2019

Language: English
Pages: 238

Cover......Page 1
De Gruyter Series in Nonlinear
Analysis and Applications......Page 3
Game Theory and
Partial Differential
Equations
......Page 5
© 2019......Page 6
Dedication......Page 7
Preface......Page 9
Acknowledgment......Page 15
Contents
......Page 17
1 Random walks and the Laplacian......Page 21
2 A first glimpse of the Tug-of-War g......Page 29
3 Tug-of-War with noise......Page 39
4 Tug-of-War......Page 63
5 Mixed boundary conditions and the obstacle
problem......Page 71
6 Maximal operators......Page 91
7 Games for eigenvalues of the Hessian......Page 121
8 Parabolic problems......Page 147
9 Free boundary problems......Page 189
A.
Viscosity solutions......Page 213
B.
Probability theory......Page 223
Bibliography......Page 227
Notations
......Page 233
Index......Page 235