Consider the following communication scenario. An encoder observes a stochastic process
and causally decides when and what to transmit about it, under a constraint on the expected …

Consider an insurance surplus process driven by a Lévy subordinator, which is observed at
discrete time points. An estimator of the Gerber–Shiu function is proposed via the empirical …

The paper considers the problem of estimating a periodic function in a continuous time
regression model observed under a general semimartingale noise with an unknown …

In this article we investigate the nonparametric estimation of the jump density of a compound
Poisson process from the discrete observation of one trajectory over [0, T]. We consider the …

In this paper, we propose a nonparametric estimator for the ruin probability in a spectrally
negative Lévy risk model based on low-frequency observation. The estimator is constructed …

Supplement to “Nonparametric implied Lévy densities”. The supplement contains the
following items:(1) limit results for the integrated squared error of the nonparametric …

Given a sample from a discretely observed Lévy process X=(Xt) t≥ 0 of the finite jump
activity, the problem of nonparametric estimation of the Lévy density ρ corresponding to the …

This article deals with adaptive nonparametric estimation for Lévy processes observed at
low frequency. For general linear functionals of the Lévy measure, we construct kernel …

Many spatiotemporal data record the time of birth and death of individuals, along with their
spatial trajectories during their lifetime, whether through continuous-time observations or …

Donsker-type functional limit theorems are proved for empirical processes arising from
discretely sampled increments of a univariate Lévy process. In the asymptotic regime the …