We consider some nonlinear integro-differential equations involving a fractional power of the Laplacian. We obtain existence and uniqueness results and associate with these equations some nonlinear singular jump-diffusion processes. We then introduce related interacting particle systems and prove propagation of chaos results, which allow to approximate numerically the solutions of the equations. The equations we are concerned with appear in the physical literature and model phenomena with anomalous diffusions.
It is a joint work with Benjamin Jourdain and Wojbor Woyczynski.