Application to the probabilistic interpretation of PDE solutions
Brownian motion and stochastic calculus
Article REF: AF566 V1
Application to the probabilistic interpretation of PDE solutions
Brownian motion and stochastic calculus

Author : Sylvie MÉLÉARD

Publication date: July 10, 2003 | Lire en français

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7. Application to the probabilistic interpretation of PDE solutions

We have just seen in Theorem23 and Proposition 12 that the infinitesimal generator (A, DA) of a diffusion process is an elliptic differential operator of order 2 (or an extension of such an operator). Thus, some probabilistic calculations are subject to partial differential equation techniques, and vice versa.

In the following, we'll say that a function f(t, x) is of class...

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