Subordinated compound Poisson processes of order k
Volume 7, Issue 4 (2020), pp. 395–413
Pub. online: 5 November 2020
Type: Research Article
Open Access
Open Access
Received
10 May 2020
10 May 2020
Revised
31 August 2020
31 August 2020
Accepted
24 October 2020
24 October 2020
Published
5 November 2020
5 November 2020
Abstract
In this article, the compound Poisson process of order k (CPPoK) is introduced and its properties are discussed. Further, using mixture of tempered stable subordinators (MTSS) and its right continuous inverse, the two subordinated CPPoK with various distributional properties are studied. It is also shown that the space and tempered space fractional versions of CPPoK and PPoK can be obtained, which generalize the process defined in [Statist. Probab. Lett. 82 (2012), 852–858].
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