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Variance Gamma (nonlocal) equations
Volume 10, Issue 4 (2023), pp. 413–424
Fausto Colantoni ORCID icon link to view author Fausto Colantoni details  

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https://doi.org/10.15559/23-VMSTA232
Pub. online: 25 September 2023      Type: Research Article      Open accessOpen Access

Received
20 February 2023
Revised
9 June 2023
Accepted
12 August 2023
Published
25 September 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.

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Keywords
Variance Gamma process fractional calculus Gamma subordinator nonlocal equations

MSC2010
60G51 34A08

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