A characterization and moving average representation for stable harmonizable processes.
Nikfar, M., Soltani, A.Reza (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Nikfar, M., Soltani, A.Reza (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Michael Hernández, Christian Houdré (1993)
Studia Mathematica
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We discuss the disjointness of two classes of stable stochastic processes: moving averages and Fourier transforms. Results on the incompatibility of these two representations date back to Urbanik. Here we extend various disjointness results to encompass larger classes of processes.
Gennady Samorodnitsky (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
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This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.
Jan Rosiński, Jennifer L. Sinclair (2010)
Banach Center Publications
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This work introduces the class of generalized tempered stable processes which encompass variations on tempered stable processes that have been introduced in the field, including "modified tempered stable processes", "layered stable processes", and "Lamperti stable processes". Short and long time behavior of GTS Lévy processes is characterized and the absolute continuity of GTS processes with respect to the underlying stable processes is established. Series representations of GTS Lévy...
Wiesław Cupała (2002)
Discussiones Mathematicae Probability and Statistics
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The Varopoulos-Hardy-Littlewood theory and the spectral analysis are used to estimate the tail of the distribution of the first exit time of α-stable processes.
Aleksander Weron (1993)
Studia Mathematica
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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...
Ken-Iti Sato, Toshiro Watanabe (2005)
Annales de l'I.H.P. Probabilités et statistiques
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Aleksander Janicki (1995)
Applicationes Mathematicae
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The aim of this paper is to apply the appropriate numerical, statistical and computer techniques to the construction of approximate solutions to nonlinear 2nd order stochastic differential equations modeling some engineering systems subject to large random external disturbances. This provides us with quantitative results on their asymptotic behavior.
Van Zanten, Harry (2008)
Electronic Communications in Probability [electronic only]
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Enrico Priola (2015)
Banach Center Publications
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We consider non-degenerate SDEs with a β-Hölder continuous and bounded drift term and driven by a Lévy noise L which is of α-stable type. If β > 1 - α/2 and α ∈ [1,2), we show pathwise uniqueness and existence of a stochastic flow. We follow the approach of [Priola, Osaka J. Math. 2012] improving the assumptions on the noise L. In our previous paper L was assumed to be non-degenerate, α-stable and symmetric. Here we can also recover relativistic and truncated stable processes and...
M. Talagrand (1989)
Annales de l'I.H.P. Probabilités et statistiques
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