TY - JOUR
T1 - On a class of multivariate counting processes
AU - Cha, Ji Hwan
AU - Giorgio, Massimiliano
N1 - Funding Information:
This work was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (grant no. 2009-0093827).
Publisher Copyright:
© 2016 Applied Probability Trust.
PY - 2016/6
Y1 - 2016/6
N2 - In this paper we define and study a new class of multivariate counting processes, named 'multivariate generalized Pólya process'. Initially, we define and study the bivariate generalized Pólya process and briefly discuss its reliability application. In order to derive the main properties of the process, we suggest some key properties and an important characterization of the process. Due to these properties and the characterization, the main properties of the bivariate generalized Pólya process are obtained efficiently. The marginal processes of the multivariate generalized Pólya process are shown to be the univariate generalized Pólya processes studied in Cha (2014). Given the history of a marginal process, the conditional property of the other process is also discussed. The bivariate generalized Pólya process is extended to the multivariate case. We define a new dependence concept for multivariate point processes and, based on it, we analyze the dependence structure of the multivariate generalized Pólya process.
AB - In this paper we define and study a new class of multivariate counting processes, named 'multivariate generalized Pólya process'. Initially, we define and study the bivariate generalized Pólya process and briefly discuss its reliability application. In order to derive the main properties of the process, we suggest some key properties and an important characterization of the process. Due to these properties and the characterization, the main properties of the bivariate generalized Pólya process are obtained efficiently. The marginal processes of the multivariate generalized Pólya process are shown to be the univariate generalized Pólya processes studied in Cha (2014). Given the history of a marginal process, the conditional property of the other process is also discussed. The bivariate generalized Pólya process is extended to the multivariate case. We define a new dependence concept for multivariate point processes and, based on it, we analyze the dependence structure of the multivariate generalized Pólya process.
KW - Complete stochastic intensity function
KW - Conditional counting process
KW - Dependence structure
KW - Marginal process
KW - Multivariate generalized Pólya process
UR - http://www.scopus.com/inward/record.url?scp=84976351607&partnerID=8YFLogxK
U2 - 10.1017/apr.2016.9
DO - 10.1017/apr.2016.9
M3 - Article
AN - SCOPUS:84976351607
SN - 0001-8678
VL - 48
SP - 443
EP - 462
JO - Advances in Applied Probability
JF - Advances in Applied Probability
IS - 2
ER -