Course on Tug-of-War Games with Random Noise

Marta Lewicka is a Polish mathematician at the University of Pittsburgh, specializing in Mathematical Analysis. Marta obtained her PhD in 2000 from Scuola Internazionale Superiore di Studi Avanzati with a thesis on Hyperbolic Systems of Conservation Laws. She has subsequently worked on Calculus of Variations, Partial Differential Equations, Continuum Mechanics, and Tug-of-War Games in relation to Nonlinear Potential Theory.

“The book is best suited for advanced graduate students and specialists in nonlinear potential theory. The author provides background appendices for probability, Brownian motion and PDEs.” (Bill Satzer, MAA Reviews, April 4, 2021)

• 1 Introduction.- 2 The linear case: random walk and harmonic functions.- 3 Tug-of-War with noise. Case p ∈ [2,∞).- 4 Boundary aware tug-of-war with noise. Case p ∈ (2,∞).- 5 Game-regularity and convergence. Case p ∈ (2,∞).- 6 Mixed tug-of-war with noise. Case p ∈ (1,∞).- A Background in probability.- B Background in Brownian motion.- C Background in PDEs. D Solutions to selected exercises.- References.- Index.