Stationarity of the Fractional Poisson process increments

Continuous Time Random Walks Limits(CTRWL) are used to model fractional diffusion processes (where Var(X_t)  is no longer proportional to t). It turns out that the fractional Poisson process(FPP) which is a generalization of the Poisson Process is a CTRWL . While the one dimensional distribution of the FPP is governed by a fractional Fokker-Planck equation, in general fractional diffusion processes are not Markovian a fact that make the process of finding its finite dimensional very complicated.  In a recent paper by Mark Meerscheart, a new method for finding the finite dimensional of CTRWL is introduced. We use this method to obtain an interesting representation of the FPP increments.