Speaker: Juan J. Manfredi, University of Pittsburgh
Time: Wednesday 9 October at 12:15—17:00
Place: MaD 302, Mattilanniemi
Department of Mathematics and Statistics at the University of Jyväskylä
Abstract:
These lectures will cover the necessary background in probability theory, discrete stochastic games, and viscosity solutions to study random tug-of-war games with noise. Below are a list of topics and a list of selected references.
(1) Probability tools: Discrete Stochastic Processes, Martingales.
(2) Viscosity Solutions. The Theorem on Sums.
(3) Asymptotic Mean Value Properties, p-Harmonious Functions.
(4) PDEs on Directed Trees.
(5) Regularity for p-harmonic functions via the Ishii-Lions method.
References:
(1) P. Blanc, J. D. Rossi, Game Theory and Partial Differential Equations. De Gruyter, 2019.
(2) P. Lindqvist, Notes on the p-Laplace Equation, BCAM Springer Briefs, 2017.
(3) A. P. Maitra, W. D. Sudderth, Discrete Gambling and Stochastic Games. Applications of Mathematics 32, Springer-Verlag, 1996.
(4) M. Parviainen, Notes on Tug-of-War Games and the p-Laplace Equation, Springer Briefs in PDE and Data Science, 2024.
(5) S.R.S. Varadan; Probability Theory, Courant Lecture Notes in Mathematics 7, New York University.
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