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.
Brownian Motion and its Applications to Mathematical Analysis Ebook
?cole d??t? de Probabilit?s 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
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