Hi all,

I think that the definition of fractional Brownian Motion is widely known (for example as a Gaussian Process with particular variance covariance stucture parametrized by the so-called Hurst index).

Heuristically, you can think of those processes as Gaussian processes with long (or short) memory depending on the value of their Hurst Index, and for Hurst index equal to 1/2 you get classical Brownian Motion (which has no memory).

I was wondering what would be the definition for "fractional Poisson Processes" and what stylised facts about fractional Brownian Motion one should consider in extending the definition to Poisson process.

If any reference exists about this, this is just fine for me.

I have no other motivation than curiosity on this topic.

Regards