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## Low-frequency estimation of continuous-time moving average Levy processes

Belomestny D., Panov V., Woerner J.

In this paper we study the problem of statistical inference for a continuous-time moving average  L\'evy process of the form

$Z_{t}=\int_{\R}\mathcal{K}(t-s)\, dL_{s},\quad t\in\mathbb{R},$  with a deterministic kernel $$\K$$ and a  L{\'e}vy process $$L$$. Especially the  estimation of  the L\'evy measure $$\nu$$ of  $L$ from low-frequency observations of the process $Z$ is considered. We construct a consistent estimator, derive its convergence rates and  illustrate its performance  by a numerical example.  On the mathematical level, we  establish  some new results on exponential mixing  for  continuous-time moving average  L\'evy processes.