Fractional Poisson Fields and Martingales

We present new properties for the Fractional Poisson process (FPP) and theFractional Poisson \ufb01eld on the plane. A martingale characterization for FPPs is given. We extend this result to Fractional Poisson \ufb01elds, obtaining some other characterizations. The fractional differential equations are studied. We consider a more general Mixed-FractionalPoisson process and show that this process is the stochastic solution of a system of fractional differential-difference equations. Finally, we give some simulations of the Fractional Poisson \ufb01eld on the plane