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.
Variance Gamma (nonlocal) equations / Colantoni, Fausto. - In: MODERN STOCHASTICS: THEORY AND APPLICATIONS. - ISSN 2351-6054. - (2023), pp. 1-12. [10.15559/23-VMSTA232]
Variance Gamma (nonlocal) equations
Fausto Colantoni
2023
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.File allegati a questo prodotto
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