EAN: 9783319043937

BROWNIAN MOTION AND ITS APPLICATIONS TO MATHEMA...

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.

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