Volume 20, 2016
|Page(s)||196 - 216|
|Published online||14 July 2016|
Statistical estimation of jump rates for a piecewise deterministic Markov processes with deterministic increasing motion and jump mechanism∗
Université de Rennes 1, Institut de Recherche mathématique de Rennes, CNRS-UMR 6625, Campus de Beaulieu, Bâtiment 22, 35042 Rennes cedex, France.
Revised: 3 May 2016
Accepted: 11 May 2016
We consider the class of Piecewise deterministic Markov processes (PDMP), whose state space is (0,∞), that possess an increasing deterministic motion and with a deterministic jump mechanism. Well known examples for this class of processes are transmission control protocol (TCP) window size process and the processes modeling the size of a “marked” Escherichia coli cell. Having observed the PDMP until its nth jump, we construct a nonparametric estimator of the jump rate λ. Our main result is that for 𝓓 a compact subset of (0,∞), if λ is in the Hölder space 𝓗s(𝓓), the squared-loss error of the estimator is asymptotically close to the speed of n− s/ (2s + 1). Simulations illustrate the behavior of our estimator.
Mathematics Subject Classification: 62M05 / 62G05 / 62G20 / 60J25
Key words: Piecewise deterministic markov processes / nonparametric estimation / jump rate estimation / ergodicity of Markov chains
© EDP Sciences, SMAI 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.