TY - JOUR
T1 - ON A MULTIVARIATE GENERALIZED POLYA PROCESS without REGULARITY PROPERTY
AU - Cha, Ji Hwan
AU - Badía, F. G.
N1 - 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.
PY - 2020/10/1
Y1 - 2020/10/1
N2 - 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.
AB - 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.
KW - characterization of multivariate counting processes
KW - complete intensity functions
KW - dependence structure
KW - generalized polya process
KW - superposition
UR - http://www.scopus.com/inward/record.url?scp=85065249370&partnerID=8YFLogxK
U2 - 10.1017/S0269964819000111
DO - 10.1017/S0269964819000111
M3 - Article
AN - SCOPUS:85065249370
SN - 0269-9648
VL - 34
SP - 484
EP - 506
JO - Probability in the Engineering and Informational Sciences
JF - Probability in the Engineering and Informational Sciences
IS - 4
ER -