Brownian Motion and its Applications to Mathematical Analysis [electronic resource] : École d'Été de Probabilités de Saint-Flour XLIII – 2013 / by Krzysztof Burdzy.
Burdzy, Krzysztof. author.
SpringerLink (Online service)
Mathematics.
Differential equations, partial.
Potential theory (Mathematics).
Distribution (Probability theory).
QA273.A1-274.9
QA274-274.9
519.2 23
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.
2014
Text
XII, 137 p. 16 illus., 4 illus. in color.
http://dx.doi.org/10.1007/978-3-319-04394-4
eng
Springer eBooks
Lecture Notes in Mathematics, 0075-8434 ; 2106
Lecture Notes in Mathematics, 0075-8434 ; 2106