Non‐Parametric Estimation of the Conditional Distribution of the Interjumping Times for Piecewise‐Deterministic Markov Processes |
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Authors: | Romain Azaïs François Dufour Anne Gégout‐Petit |
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Affiliation: | 1. Inria Bordeaux Sud‐Ouest, , Team CQFD, France;2. Institut de Mathématiques de Bordeaux |
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Abstract: | This paper presents a non‐parametric 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 study illustrates the behaviour of our estimator. |
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Keywords: | piecewise‐deterministic Markov process ergodicity of Markov chains non‐parametric estimation jump rate estimation Nelson– Aalen estimator asymptotic consistency |
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