Titlebook: A Course on Tug-of-War Games with Random Noise; Introduction and Bas Marta Lewicka Textbook 2020 The Editor(s) (if applicable) and The Auth

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0172-5939 g the book suitable as a textbook for a graduate course, as well as for self-study. Extensive background and auxiliary material allow the tailoring of courses to individual student levels..978-3-030-46208-6978-3-030-46209-3Series ISSN 0172-5939 Series E-ISSN 2191-6675

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Modern Agencies — The Ideal Typeaplace’s equation and harmonic functions, construction of the ball walk, values of the ball walk as harmonic functions, walk-regularity of boundary points, the exterior cone condition as sufficient for walk-regularity, relation to Perron solutions and relation to Brownian motion.

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https://doi.org/10.1057/9780230504868he following topics are covered: the averaging principle and the dynamic programming principle for the ellipsoid-distributed noise, the mixed Tug-of-War and two sufficient conditions for game-regularity: the exterior corkscrew condition and the simply connectedness in dimension .?=?2.

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Front Matterm their vacuum values to the bulk values. We recognise three ill-defined regions (in the sense that their edges are not sharp), which are important in determining the optical response of a surface: I the vacuum region; II the (narrow) selvedge region; HI the bulk. Since the advent of modern surface