Introduction to Random Tug-of-War Games and PDEs

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2045)

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.

Keywords

Harmonic Function Stochastic Game Dynamic Programming Principle Maximal Theorem Strong Comparison Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA

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