Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes

Romain Azaïs 1, 2 François Dufour 1, 2 Anne Gégout-Petit 1, 2
2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a long time interval. Our method relies on a generalization of Aalen's multiplicative intensity model. We prove the uniform consistency of our estimator, under some reasonable assumptions related to the primitive characteristics of the process. A simulation example illustrates the behavior of our estimator.
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https://hal.archives-ouvertes.fr/hal-00759064
Contributor : Romain Azaïs <>
Submitted on : Thursday, November 29, 2012 - 11:05:19 PM
Last modification on : Wednesday, January 23, 2019 - 1:20:03 PM

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  • HAL Id : hal-00759064, version 1
  • ARXIV : 1202.2212

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Romain Azaïs, François Dufour, Anne Gégout-Petit. Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes. 2012. ⟨hal-00759064⟩

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