Brownian Motion and the Heat Equation

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


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


Initial Data Brownian Motion Lebesgue Measure Heat Equation Dirichlet Boundary 
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    A. Fasano, Mathematical models of some diffusive processes with free boundaries. SIMAI e-Lecture Notes (2008)Google Scholar
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    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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