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Pré-Publication, Document De Travail Année : 2017

Estimation of the average number of continuous crossings for non-stationary non-diffusion processes

Résumé

Assume that you observe trajectories of a non-diffusive non-stationary process and that you are interested in the average number of times where the process crosses some threshold (in dimension d = 1) or hypersurface (in dimension d ≥ 2). Of course, you can actually estimate this quantity by its empirical version counting the number of observed crossings. But is there a better way? In this paper, for a wide class of piecewise smooth processes, we propose estimators of the average number of continuous crossings of an hypersurface based on Kac-Rice formulae. We revisit these formulae in the uni-and multivariate framework in order to be able to handle non-stationary processes. Our statistical method is tested on both simulated and real data.
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Dates et versions

hal-01499914 , version 1 (01-04-2017)
hal-01499914 , version 2 (03-11-2017)
hal-01499914 , version 3 (13-04-2018)

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Citer

Romain Azaïs, Alexandre Genadot. Estimation of the average number of continuous crossings for non-stationary non-diffusion processes. 2017. ⟨hal-01499914v2⟩

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