Information-based thinning of point processes and its application to shock models

Ji Hwan Cha; Maxim Finkelstein

doi:10.1016/j.jspi.2012.02.049

Information-based thinning of point processes and its application to shock models

Ji Hwan Cha, Maxim Finkelstein

Department of Statistics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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.

Original language	English
Pages (from-to)	2345-2350
Number of pages	6
Journal	Journal of Statistical Planning and Inference
Volume	142
Issue number	8
DOIs	https://doi.org/10.1016/j.jspi.2012.02.049
State	Published - Aug 2012

Bibliographical note

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 .

Keywords

Conditional intensity
History-dependent thinning
Partial information
Shock model
Thinning of point processes

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10.1016/j.jspi.2012.02.049

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title = "Information-based thinning of point processes and its application to shock models",

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.",

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note = "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 .",

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AU - Finkelstein, Maxim

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KW - Partial information

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Information-based thinning of point processes and its application to shock models

Abstract

Bibliographical note

Keywords

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