Variance Gamma (non-local) equations
Probability
2022-10-19 v1
Abstract
We provide some equations for the Variance Gamma process due to the fact that we do not consider only the definition as a time-changed Brownian motion. This brings us to a new non-local equation, even true in the drifted case, involving generalized Weyl derivatives. Then we focus on the connection to special functions and we study a space equation for our process. At the end, we conclude by observing the convergence in distribution of a compound Poisson process to the Variance Gamma process.
Cite
@article{arxiv.2210.09816,
title = {Variance Gamma (non-local) equations},
author = {Fausto Colantoni},
journal= {arXiv preprint arXiv:2210.09816},
year = {2022}
}