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Brownian Motion and its Applications to Mathematical Analysis École d'Été de Probabilités de Saint-Flour XLIII – 2013 /

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, su...

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Hlavní autor: Burdzy, Krzysztof. (Autor, http://id.loc.gov/vocabulary/relators/aut)
Korporativní autor: SpringerLink (Online service)
Médium: Elektronický zdroj E-kniha
Jazyk:English
Vydáno: Cham : Springer International Publishing : Imprint: Springer, 2014.
Vydání:1st ed. 2014.
Edice:École d'Été de Probabilités de Saint-Flour, 2106
Témata:
Probabilities.
Partial differential equations.
Potential theory (Mathematics).
Probability Theory and Stochastic Processes.
Partial Differential Equations.
Potential Theory.
On-line přístup:https://doi.org/10.1007/978-3-319-04394-4
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Obsah:
  • 1. Brownian motion
  • 2. Probabilistic proofs of classical theorems
  • 3. Overview of the "hot spots" problem
  • 4. Neumann eigenfunctions and eigenvalues
  • 5. Synchronous and mirror couplings
  • 6. Parabolic boundary Harnack principle
  • 7. Scaling coupling
  • 8. Nodal lines
  • 9. Neumann heat kernel monotonicity
  • 10. Reflected Brownian motion in time dependent domains.

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