Format:
1 Online-Ressource (XII, 137 S.)
,
Ill., graph. Darst.
ISBN:
9783319043944
Series Statement:
Lecture notes in mathematics 2106
Content:
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
Additional Edition:
Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-3-319-04393-7
Language:
English
Subjects:
Mathematics
Keywords:
Brownsche Bewegung
;
Analysis
;
Beweis
;
Mathematik
;
Partielle Differentialgleichung
DOI:
10.1007/978-3-319-04394-4
