PDE Problems and Diffusions
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.
- Azencott, R. and al. (1981). Géodésiques et Diffusions en temps petit. Astérisque 84–85.Google Scholar