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

Abstract

The \(\alpha \)-stable L\(\acute{\mathrm{e}}\)vy motion together with the Poisson process and Brownian motion are the most important examples of L\(\acute{\mathrm{e}}\)vy processes, which form the first class of stochastic processes being studied in the modern spirit. In this paper, the stochastic processes driven by \(\alpha \)-stable L\(\acute{\mathrm{e}}\)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.