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A minimal contrast estimator for the linear fractional stable motion. (English) Zbl 1454.60052

The authors study the linear fractional stable motion with three-dimensional parameters \((\sigma,\alpha,H)\), where \(H\) represents the self-similarity parameter and \((\sigma,\alpha)\) are the scaling and stability parameters of the driving symmetric Lévy process \(L\). In this paper, an estimator of this process is established. The main result investigates the strong consistency and weak limit theorems for the resulting estimator. Several ideas were used before in the papers: [the authors, Springer Proc. Math. Stat. 294, 41–56 (2019; Zbl 1434.62031)] and [S. Mazur et al., Bernoulli 26, No. 1, 226–252 (2020; Zbl 1453.60088)], in which the parameter estimation for the linear fractional stable motion and related Lévy moving average processes were studied.

MSC:

60G22 Fractional processes, including fractional Brownian motion
62F12 Asymptotic properties of parametric estimators
62E20 Asymptotic distribution theory in statistics
60E07 Infinitely divisible distributions; stable distributions
60F05 Central limit and other weak theorems
60G10 Stationary stochastic processes

Software:

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References:

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