Click Here to Download: https://ouo.io/hZCG7O Brownian Motion and its Applications to Mathematical Analysis École d'Été de Probabilités de Saint-Flour XLIII – 2013 By: Krzysztof Burdzy Publisher: Springer Print ISBN: 9783319043937, 3319043935 eText ISBN: 9783319043944, 3319043943 Copyright year: 2014 Format: EPUB Available from $ 54.99 USD SKU 9783319043944 These 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 domains.
