TY - JOUR
T1 - Information-based thinning of point processes and its application to shock models
AU - Cha, Ji Hwan
AU - Finkelstein, Maxim
N1 - Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0017338 ). The work of the second author was supported by the National Research Foundation of South Africa (NRF) grant FA2006040700002 .
PY - 2012/8
Y1 - 2012/8
N2 - Thinning of point processes is a useful operation that is implemented in various stochastic models. When the initial point process is the nonhomogeneous Poisson process (NHPP), the thinned processes are also nonhomogeneous Poisson processes independent of each other. The crucial assumption in deriving this result is that the corresponding classification of events is independent of all other events, including the history of the process. However, in practice, this classification is often dependent on the history. In our paper, we define and describe the thinned processes for the history-dependent case using different levels of available information. We also discuss the applications of the obtained general results to the corresponding shocks models.
AB - Thinning of point processes is a useful operation that is implemented in various stochastic models. When the initial point process is the nonhomogeneous Poisson process (NHPP), the thinned processes are also nonhomogeneous Poisson processes independent of each other. The crucial assumption in deriving this result is that the corresponding classification of events is independent of all other events, including the history of the process. However, in practice, this classification is often dependent on the history. In our paper, we define and describe the thinned processes for the history-dependent case using different levels of available information. We also discuss the applications of the obtained general results to the corresponding shocks models.
KW - Conditional intensity
KW - History-dependent thinning
KW - Partial information
KW - Shock model
KW - Thinning of point processes
UR - http://www.scopus.com/inward/record.url?scp=84859573455&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2012.02.049
DO - 10.1016/j.jspi.2012.02.049
M3 - Article
AN - SCOPUS:84859573455
SN - 0378-3758
VL - 142
SP - 2345
EP - 2350
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 8
ER -