A Point Process Approach to Filtered Processes

被引：0

作者：

Julien Michel

机构：

[1] Unité de Mathématiques Pures et Appliquées—UMR 5669,

[2] ENS Lyon,undefined

来源：

Methodology And Computing In Applied Probability | 2004年 / 6卷

关键词：

point processes; simulation; estimation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider some models of filtered point processes such as those developped in Yue and Hashino (2001), and rephrase them in terms of point processes. We derive from this formulation some estimates for the probability of overflow in a rainfall process. This method allows us by considering a non deterministic model of filtering to compute some characteristics of the compound models of Cowpertwait (1994), Phelan (1991), and Rodriguez-Iturbe et al. (1987, 1988). A spatial version of this point process is also studied, using an analogy with the boolean model of stochastic geometry we compute bounds for the probability of dryness in a compound rainfall process.

引用

页码：423 / 440

页数：17

共 10 条

[1] Cowpertwait P. S. P.(1994)A generalized point process model for rainfall Proc. Roy. Soc. London Ser. A 447 23-37
[2] Kendall D. G.(1949)Stochastic processes and population growth J. Roy. Statist. Soc. B 230-264
[3] Rodriguez-Iturbe I.(1987)Some models for rainfall based on stochastic point processes Proc. Roy. Soc. London Ser. A 410 269-288
[4] Cox D. R.(1988)A point process model for rainfall: Further developments Proc. Roy. Soc. London Ser. A 417 283-298
[5] Isham V.(2001)The general cumulants for a filtered point process Appl. Math. Mod. 25 193-201
[6] Rodriguez-Iturbe I.(undefined)undefined undefined undefined undefined-undefined
[7] Cox D. R.(undefined)undefined undefined undefined undefined-undefined
[8] Isham V.(undefined)undefined undefined undefined undefined-undefined
[9] Yue S.(undefined)undefined undefined undefined undefined-undefined
[10] Hashino M.(undefined)undefined undefined undefined undefined-undefined

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