Displaying similar documents to “Estimation of the spectral density of a homogeneous random stable discrete time field.”

Statistical estimation of higher-order spectral densities by means of general tapering

M'hammed Baba Harra (1997)

Applicationes Mathematicae

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Given a realization on a finite interval of a continuous-time stationary process, we construct estimators for higher order spectral densities. Tapering and shift-in-time methods are used to build estimators which are asymptotically unbiased and consistent for all admissible values of the argument. Asymptotic results for the fourth-order densities are given. Detailed attention is paid to the nth order case.

Geometric Stable Laws Through Series Representations

Kozubowski, Tomasz, Podgórski, Krzysztof (1999)

Serdica Mathematical Journal

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Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study...

Approximation of finite-dimensional distributions for integrals driven by α-stable Lévy motion

Aleksander Janicki (1999)

Applicationes Mathematicae

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We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems...