A new characterization of the jump rate for piecewise-deterministic Markov processes with discrete transitions. Issue 8 (18th April 2018)

• Record Type: Journal Article
• Authors: Azaïs, Romain; Genadot, Alexandre
• Is Part Of: Communications in statistics. Volume 47:Issue 8(2018)
• Page Start: 1812
• Page End: 1829
• Publication Date: 2018-04-18
• Subjects: Discrete transitions -- estimation -- jump rate -- piecewise-deterministic Markov process.; 62M05 -- 62G05; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1327072
• Languages: English
• ISSNs: 0361-0926

Abstract

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.