TY - JOUR
T1 - A new class of multivariate counting processes and its characterization
AU - Cha, Ji Hwan
AU - Giorgio, Massimiliano
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).
Publisher Copyright:
© 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019/4/3
Y1 - 2019/4/3
N2 - In this paper, we suggest a new class of multivariate counting processes which generalizes and extends the multivariate generalized Polya process recently studied in Cha and Giorgio [On a class of multivariate counting processes, Adv. Appl. Probab. 48 (2016), pp. 443–462]. Initially, we define this multivariate counting process by means of mixing. For further characterization of it, we suggest an alternative definition, which facilitates convenient characterization of the proposed process. We also discuss the dependence structure of the proposed multivariate counting process and other stochastic properties such as the joint distributions of the number of events in an arbitrary interval or disjoint intervals and the conditional joint distribution of the arrival times of different types of events given the number of events. The corresponding marginal processes are also characterized.
AB - In this paper, we suggest a new class of multivariate counting processes which generalizes and extends the multivariate generalized Polya process recently studied in Cha and Giorgio [On a class of multivariate counting processes, Adv. Appl. Probab. 48 (2016), pp. 443–462]. Initially, we define this multivariate counting process by means of mixing. For further characterization of it, we suggest an alternative definition, which facilitates convenient characterization of the proposed process. We also discuss the dependence structure of the proposed multivariate counting process and other stochastic properties such as the joint distributions of the number of events in an arbitrary interval or disjoint intervals and the conditional joint distribution of the arrival times of different types of events given the number of events. The corresponding marginal processes are also characterized.
KW - characterization of multivariate counting processes
KW - complete intensity functions
KW - mixing
KW - Multivariate generalized Polya process
KW - restarting property
UR - http://www.scopus.com/inward/record.url?scp=85056180650&partnerID=8YFLogxK
U2 - 10.1080/17442508.2018.1540625
DO - 10.1080/17442508.2018.1540625
M3 - Article
AN - SCOPUS:85056180650
SN - 1744-2508
VL - 91
SP - 383
EP - 406
JO - Stochastics
JF - Stochastics
IS - 3
ER -