Abstract
Some equations are provided for the Variance Gamma process using the definition other than that based on a time-changed Brownian motion. A new nonlocal equation is obtained involving generalized Weyl derivatives, which is true even in the drifted case. The connection to special functions is in focus, and a space equation for the process is studied. In conclusion, the convergence in distribution of a compound Poisson process to the Variance Gamma process is observed.
Subject
Statistics, Probability and Uncertainty,Modeling and Simulation,Statistics and Probability
Reference25 articles.
1. Foreign exchange options on Heston-CIR model under Lévy process framework;Appl. Math. Comput.,2023
2. Geometric stable processes and related fractional differential equations;Electron. Commun. Probab.,2014
3. Diffusion equation and stochastic processes;Proc. Natl. Acad. Sci.,1949