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Tug-of-war games and PDEs

Published online by Cambridge University Press:  04 April 2011

Julio D. Rossi
Affiliation:
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentinajrossi@dm.uba.ar

Abstract

We review some recent results concerning tug-of-war games and their relation to some well-known partial differential equations (PDEs). In particular, we will show that solutions to certain PDEs can be obtained as limits of values of tug-of-war games when the parameter that controls the length of the possible movements goes to zero. Since the equations being studied are nonlinear and are not in divergence form, we will make extensive use of the concept of viscosity solutions.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2011

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