A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions |
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Authors: | Romain Azaïs Alexandre Genadot |
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Affiliation: | 1. Inria Nancy – Grand Est, Team BIGS and Institut élie Cartan de Lorraine, Nancy, France;2. Institut de Mathématiques de Bordeaux and Inria Bordeaux – Sud Ouest, Team CQFD |
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Abstract: | Piecewise-deterministic Markov processes form a general class of non diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate of such a process with discrete transitions. We deduce from this result a non parametric technique for estimating this feature of interest. We state the uniform convergence in probability of the estimator. The methodology is illustrated on a numerical example. |
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Keywords: | Discrete transitions estimation jump rate piecewise-deterministic Markov process. |
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