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Brownian Motion and the Heat Equation

  • Gioia CarinciEmail author
  • Anna De Masi
  • Cristian Giardinà
  • Errico Presutti
Chapter
Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 12)

Abstract

The proof of Theorem  3.2 uses extensively a representation of the solution of the heat equation in terms of Brownian motions.

Keywords

Initial Data Brownian Motion Lebesgue Measure Heat Equation Dirichlet Boundary 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    D. Revuz, M. Yor, Continuous martingales and Brownian motion, Grundlehren der Mathematischen Wissenschaften, vol. 293, 3rd edn. (Springer, Berlin, 1999)Google Scholar
  2. 2.
    A. Fasano, Mathematical models of some diffusive processes with free boundaries. SIMAI e-Lecture Notes (2008)Google Scholar
  3. 3.
    G. Peskir, A. Shiryaev, Optimal stopping and Free-boundary problems. Lecture in Mathematics ETH Zürich Birkhuser (2006)Google Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Gioia Carinci
    • 1
    Email author
  • Anna De Masi
    • 2
  • Cristian Giardinà
    • 3
  • Errico Presutti
    • 4
  1. 1.Delft University of TechnologyDelftThe Netherlands
  2. 2.Dipartimento di MatematicaUniversita di L’AguilaL’AquilaItaly
  3. 3.Dipartimento di MatematicaUniversità di Modena e Reggio EmiliaModenaItaly
  4. 4.Gran Sasso Science InstituteL’AquilaItaly

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