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PDE Problems and Diffusions

  • Paolo Baldi
Chapter
Part of the Universitext book series (UTX)

Abstract

In this chapter we see that the solutions of some PDE problems can be represented as expectations of functionals of diffusion process. These formulas are very useful from two points of view. First of all, for the investigation and a better understanding of the properties of the solutions of these PDEs. Moreover, in some situations, they allow to compute the solution of the PDE (through the explicit computation of the expectation of the corresponding functional) or the expectation of the functional (by solving the PDE explicitly). The exercises of this chapter and Exercise 12.8 provide some instances of this way of reasoning.

References

  1. Azencott, R. and al. (1981). Géodésiques et Diffusions en temps petit. Astérisque 84–85.Google Scholar
  2. Friedman, A. (1964). Partial Differential Equations of Parabolic Type. Prentice Hall.zbMATHGoogle Scholar
  3. Friedman, A. (1975). Stochastic Differential Equations and Applications, I and II. Academic Press, New York.zbMATHGoogle Scholar
  4. Levi, E. E. (1907). Sulle equazioni lineari totalmente ellittiche alle derivate parziali. Rend. Circolo. Mat. Palermo, 24:275–317.CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Paolo Baldi
    • 1
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly

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