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Nadaraya-Watson estimator for stochastic processes driven by stable Lévy motions. (English) Zbl 1337.62204
Summary: We discuss the nonparametric Nadaraya-Watson (N-W) estimator of the drift function for ergodic stochastic processes driven by $$\alpha$$-stable noises and observed at discrete instants. Under geometrical mixing condition, we derive consistency and rate of convergence of the N-W estimator of the drift function. Furthermore, we obtain a central limit theorem for stable stochastic integrals. The central limit theorem has its own interest and is the crucial tool for the proofs. A simulation study illustrates the finite sample properties of the N-W estimator.

##### MSC:
 62M05 Markov processes: estimation; hidden Markov models 62G05 Nonparametric estimation 62G07 Density estimation 60G52 Stable stochastic processes 62G20 Asymptotic properties of nonparametric inference 65C30 Numerical solutions to stochastic differential and integral equations
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