Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1149544 | Journal of Statistical Planning and Inference | 2012 | 6 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Ji Hwan Cha, Maxim Finkelstein,