Self-decomposability of weak variance generalised gamma convolutions

Boris Buchmann, Kevin W. Lu and Dilip B. Madan

Stochastic Processes and their Applications, 2020, vol. 130, issue 2, 630-655

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.

Keywords: Bessel function; Brownian motion; Generalised gamma convolutions; Hadamard product; Infinite divisibility; Lévy process; Multivariate subordination; Self-decomposability; Thorin measure; Weak subordination; Variance-gamma; Variance generalised gamma convolution (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2019.02.012

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