×

Parameter estimation for a class of stochastic differential equations driven by small stable noises from discrete observations. (English) Zbl 1240.62005

Summary: We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small \(\alpha\)-stable noises, observed at \(n\) regularly spaced time points \(t_i=i/n,i=1,\cdots, n\) on \([0,1]\). Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator (LSE) when a small dispersion parameter \(\varepsilon \to 0\) and \(n\to \infty\) simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.

MSC:

62M05 Markov processes: estimation; hidden Markov models
60G52 Stable stochastic processes
60J75 Jump processes (MSC2010)
62F12 Asymptotic properties of parametric estimators
62F10 Point estimation
PDFBibTeX XMLCite
Full Text: DOI