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Least squares estimators for stochastic differential equations driven by small Lévy noises

Hongwei Long, Chunhua Ma and Yasutaka Shimizu

Stochastic Processes and their Applications, 2017, vol. 127, issue 5, 1475-1495

Abstract: We study parameter estimation for discretely observed stochastic differential equations driven by small Lévy noises. We do not impose Lipschitz condition on the dispersion coefficient function σ and any moment condition on the driving Lévy process, which greatly enhances the applicability of our results to many practical models. Under certain regularity conditions on the drift and dispersion functions, we obtain consistency and rate of convergence of the least squares estimator (LSE) of parameter when ε→0 and n→∞ simultaneously. We present some simulation study on a two-factor financial model driven by stable noises.

Keywords: Asymptotic distribution; Consistency; Discrete observations; Least squares method; Stochastic differential equations; Parameter estimation (search for similar items in EconPapers)
Date: 2017
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Handle: RePEc:eee:spapps:v:127:y:2017:i:5:p:1475-1495