Self-decomposability of weak variance generalised gamma convolutions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Buchmann, Boris¹  Lu, Kevin W.¹  Madan, Dilip B.² 

[1] Australian Natl Univ, Res Sch Finance Actuarial Studies & Stat, Canberra, ACT 0200, Australia

[2] Univ Maryland, Robert H Smith Sch Business, College Pk, MD 20742 USA

关键词: Bessel function;    Brownian motion;    Generalised gamma convolutions;    Hadamard product;    Infinite divisibility;    Levy process;    Multivariate subordination;    Self-decomposability;    Thorin measure;    Weak subordination;    Variance-gamma;    Variance generalised gamma convolution;   

DOI  :  10.1016/j.spa.2019.02.012

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free