Selfdecomposability of Weak Variance Generalised Gamma Convolutions

2017/12/11 by Boris Buchmann, Buchmann, Boris, Kevin W. Lu +3 · 1 citation
Economics, Econometrics and Finance · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1712.03640

openalex publication_date 2017/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Weak variance generalised gamma convolution processes are multivariate Brownian motions weakly subordinated by multivariate Thorin subordinators. Within this class, we extend a result from strong to weak subordination that a driftless Brownian motion gives rise to a self-decomposable process. Under moment conditions on the underlying Thorin measure, we show that this condition is also necessary. We apply our results to some prominent processes such as the weak variance alpha-gamma process, and illustrate the necessity of our moment conditions in some cases.

Cited by

• Infinite divisibility of α-Cauchy distributions

Related

• Weak Subordination of Multivariate Lévy Processes and Variance Generalised Gamma Convolutions
• Calibration for Weak Variance-Alpha-Gamma Processes
• Thorin processes and their subordination
• Some characterizations of multiple selfdecomposability with extensions and an application to the Gamma function
• Natural decomposition of processes and weak Dirichlet processes