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60H30 Probability theory and stochastic processes -- Stochastic analysis -- Applications of stochastic analysis (to PDE, etc.)

60G17 Probability theory and stochastic processes -- Stochastic processes -- Sample path properties

58J65 Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Diffusion processes and stochastic analysis on manifolds En-ligne: Sommaire | Zentralblatt

Location | Call Number | Status | Date Due |
---|---|---|---|

Salle S | 12283-01 / Ecole STF (Browse Shelf) | Available |

Bibliogr. p. 133-137

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. (Source : Springer)

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