Local linear estimation for stochastic processes driven by $$\alpha $$ α -stable L $$\acute{\mathbf{e}}$$ e ´ vy motion

Yunyan Wang () and Lixin Zhang ()

Statistical Inference for Stochastic Processes, 2013, vol. 16, issue 2, 171 pages

Abstract: The $$\alpha $$ α -stable L $$\acute{\mathrm{e}}$$ e ´ vy motion together with the Poisson process and Brownian motion are the most important examples of L $$\acute{\mathrm{e}}$$ e ´ vy processes, which form the first class of stochastic processes being studied in the modern spirit. In this paper, the stochastic processes driven by $$\alpha $$ α -stable L $$\acute{\mathrm{e}}$$ e ´ vy motion are considered, local linear estimator of the drift function for these processes is discussed. Under mild conditions, we derive consistency of the local linear estimator of the drift function. The performance of the proposed estimator is assessed by simulation study. Copyright Springer Science+Business Media Dordrecht 2013

Keywords: Lévy motion; Local linear estimator; Nadaraya–Watson estimator; Stochastic differential equation (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:16:y:2013:i:2:p:161-171

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DOI: 10.1007/s11203-013-9080-3

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