On convergence in some subspaces of generalized functions
S. Pilipović (1979)
Matematički Vesnik
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S. Pilipović (1979)
Matematički Vesnik
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Djamel Hamadouche, Charles Suquet (1999)
Applicationes Mathematicae
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We consider stochastic processes as random elements in some spaces of Hölder functions vanishing at infinity. The corresponding scale of spaces is shown to be isomorphic to some scale of Banach sequence spaces. This enables us to obtain some tightness criterion in these spaces. As an application, we prove the weak Hölder convergence of the convolution-smoothed empirical process of an i.i.d. sample under a natural assumption about the regularity of the marginal distribution function...
Aleksander Janicki, Zbigniew Michna, Aleksander Weron (1997)
Applicationes Mathematicae
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In this paper we present a result on convergence of approximate solutions of stochastic differential equations involving integrals with respect to α-stable Lévy motion. We prove an appropriate weak limit theorem, which does not follow from known results on stability properties of stochastic differential equations driven by semimartingales. It assures convergence in law in the Skorokhod topology of sequences of approximate solutions and justifies discrete time schemes applied in computer...
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...
Kouji Yano, Yuko Yano, Marc Yor (2010)
Annales de l'I.H.P. Probabilités et statistiques
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Penalisation involving the one-sided supremum for a stable Lévy process with index ∈(0, 2] is studied. We introduce the analogue of Azéma–Yor martingales for a stable Lévy process and give the law of the overall supremum under the penalised measure.
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...
François Coquet, Jean Mémin (1998)
Publications mathématiques et informatique de Rennes
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Bruno Morel (2004)
Studia Mathematica
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We prove invariance principles for partial sum processes in Besov spaces. This functional framework allows us to give a unified treatment of the step process and the smoothed process in the same parametric scale of function spaces. Our functional central limit theorems in Besov spaces hold for i.i.d. sequences and also for a large class of weakly dependent sequences.
Agratini, Octavian (1998)
General Mathematics
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John R. Baxter, Rafael V. Chacon (1989)
Séminaire de probabilités de Strasbourg
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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.
Budsaba, Kamon, Chen, Pingyan, Volodin, Andrei (2007)
Lobachevskii Journal of Mathematics
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B. Choczewski (1971)
Annales Polonici Mathematici
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