02612nam a2200361 a 4500991002949319707536160721t20142014sz a b 000 0 eng d9783319043937b14258845-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng530.47523AMS 60-02AMS 60G17AMS 60H30AMS 60J65LC QA274.75.B87Burdzy, Krzysztof59868Brownian motion and its applications to mathematical analysis :École d'été de probabilités de Saint-Flour XLIII - 2013 /Krzysztof BurdzyCham [Switzerland] :Springer,c2014xii, 137 p. :ill. (some color) ;24 cmLecture notes in mathematics,0075-8434 ;21061.Brownian motion ;2.Probabilistic proofs of classical theorems ;3.Overview of the "hot spots" problem ;4.Neumann eigenfunctions and eigenvalues ;5.Synchronous and mirror couplings ;6.Parabolic boundary Harnack principle ;7.Scaling coupling ;8.Nodal lines ;9.Neumann heat kernel monotonicity ;10.Reflected Brownian motion in time dependent domainsThese lecture notes provide an introduction to the applications of Brownian motion to analysis and, more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics. The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis. The bulk of the notes are devoted to recent (post-1990) applications of stochastic analysis to Neumann eigenfunctions, Neumann heat kernel and the heat equation in time-dependent domainsBrownian motion processesMathematical analysisStochastic analysisÉcole d'été de probabilités de Saint-Flour<43. ;2013 ;Saint Flour, France>.b1425884511-11-1621-07-16991002949319707536LE013 60-XX BUR11 (2014)12013000293479le013pE36.39-l- 00000.i1578703511-11-16Brownian motion and its applications to mathematical analysis821272UNISALENTOle01321-07-16ma -engsz 00