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Brownian Motion and its Applications to Mathematical Analysis

Brownian Motion and its Applications to Mathematical Analysis

Krzysztof Burdzy

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Editorial:
Springer Nature B.V.
Año de edición:
2014
Materia
Probabilidad y estadística
ISBN:
9783319043937
62,04 €
IVA incluido
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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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