Abstract
Most of the multivariate counting processes studied in the literature are regular processes, which implies, ignoring the types of the events, the non-occurrence of multiple events. However, in practice, several different types of events may occur simultaneously. In this paper, a new class of multivariate counting processes which allow simultaneous occurrences of multiple types of events is suggested and its stochastic properties are studied. For the modeling of such kind of process, we rely on the tool of superposition of seed counting processes. It will be shown that the stochastic properties of the proposed class of multivariate counting processes are explicitly expressed. Furthermore, the marginal processes are also explicitly obtained. We analyze the multivariate dependence structure of the proposed class of counting processes.
Original language | English |
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Pages (from-to) | 484-506 |
Number of pages | 23 |
Journal | Probability in the Engineering and Informational Sciences |
Volume | 34 |
Issue number | 4 |
DOIs | |
State | Published - 1 Oct 2020 |
Bibliographical note
Funding Information:The work of the first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211). The work of the second author has been supported by Spanish government research project MTM2015- 63978(MINECO/FEDER).
Publisher Copyright:
© Cambridge University Press 2019.
Keywords
- characterization of multivariate counting processes
- complete intensity functions
- dependence structure
- generalized polya process
- superposition