03137nam 22005895 450 991048389960332120200706003126.03-030-46209-910.1007/978-3-030-46209-3(CKB)5310000000016544(MiAaPQ)EBC6231722(DE-He213)978-3-030-46209-3(PPN)248595768(EXLCZ)99531000000001654420200619d2020 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA Course on Tug-of-War Games with Random Noise[electronic resource] Introduction and Basic Constructions /by Marta Lewicka1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (ix, 254 pages) illustrationsUniversitext,0172-59393-030-46208-0 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.This graduate textbook provides a detailed introduction to the probabilistic interpretation of nonlinear potential theory, relying on the recently introduced notion of tug-of-war games with noise. The book explores both basic and more advanced constructions, carefully explaining the parallel between linear and nonlinear cases. The presentation is self-contained with many exercises, making 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.Universitext,0172-5939Potential theory (Mathematics)ProbabilitiesMathematical analysisAnalysis (Mathematics)Potential Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12163Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Potential theory (Mathematics).Probabilities.Mathematical analysis.Analysis (Mathematics).Potential Theory.Probability Theory and Stochastic Processes.Analysis.515.7Lewicka Martaauthttp://id.loc.gov/vocabulary/relators/aut867035MiAaPQMiAaPQMiAaPQBOOK9910483899603321A Course on Tug-of-War Games with Random Noise1935244UNINA