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Title:

Lévy Copulas: Dynamics and Transforms of Upsilon Type

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Lévy processes and infinitely divisible distributions are increasingly defined in terms of their Lévy measure. In order to describe the dependence structure of a multivariate Lévy measure, Tankov (2003) introduced Lévy copulas on <file name="sjos_527_mu1.gif" type="gif" /> . (For an extension to R -super- ""m"" , see Kallsen & Tankov, 2006.)...

Lévy processes and infinitely divisible distributions are increasingly defined in terms of their Lévy measure. In order to describe the dependence structure of a multivariate Lévy measure, Tankov (2003) introduced Lévy copulas on <file name="sjos_527_mu1.gif" type="gif" /> . (For an extension to R -super- ""m"" , see Kallsen & Tankov, 2006.) Together with the marginal Lévy measures they completely describe multivariate Lévy measures on <file name="sjos_527_mu2.gif" type="gif" /> . In this article we show that any such Lévy copula defines itself a Lévy measure with one-stable margins, in a canonical way. A limit theorem is obtained, characterizing convergence of Lévy measures with the aid of Lévy copulas. Homogeneous Lévy copulas are considered in detail. They correspond to Lévy processes which have a time-constant Lévy copula, and a complete description of homogeneous Lévy copulas is obtained. A general scheme to construct multivariate distributions having special properties is outlined, for distributions with prescribed margins having the same properties. This makes use of Lévy copulas and of certain mappings of Upsilon type. The construction is then exemplified for distributions in the Goldie-Steutel-Bondesson class, the Thorin class and for self-decomposable distributions. Copyright 2007 Board of the Foundation of the Scandinavian Journal of Statistics. Minimize

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Title:

Stationarity, mixing, distributional properties and moments of GARCH(p, q

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Abstract This paper collects some of the well known probabilistic properties of GARCH(p, q) processes. In particular, we address the question of strictly and of weakly stationary solutions. We further investigate moment conditions as well as the strong mixing property of GARCH processes. Some distributional properties such as the tail behaviour ...

Abstract This paper collects some of the well known probabilistic properties of GARCH(p, q) processes. In particular, we address the question of strictly and of weakly stationary solutions. We further investigate moment conditions as well as the strong mixing property of GARCH processes. Some distributional properties such as the tail behaviour and continuity properties of the stationary distribution are also included. 1 Minimize

Publisher:

Springer

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-23

Source:

http://www-m4.ma.tum.de/pers/lindner/lindner4.pdf

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text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

On Lower Bounds of Exponential Frames

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-12

Source:

http://www-m4.ma.tum.de/pers/lindner/lindnerpaper1.pdf

Document Type:

text

Language:

en

Subjects:

lower bound ; exponential frame ; sine-type-function ; irregular sampling

lower bound ; exponential frame ; sine-type-function ; irregular sampling Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

On Lower Bounds of Exponential Frames

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Lower frame bounds for sequences of exponentials are obtained in a special version of Avdonin's theorem on "1/4 in the mean" (1974) and in a theorem of Dun and Schaeer (1952). Keywords: lower bound, exponential frame, sine-type-function, irregular sampling

Lower frame bounds for sequences of exponentials are obtained in a special version of Avdonin's theorem on "1/4 in the mean" (1974) and in a theorem of Dun and Schaeer (1952). Keywords: lower bound, exponential frame, sine-type-function, irregular sampling Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-15

Source:

http://www-m4.mathematik.tu-muenchen.de/m4/pers/lindner/lindnerpaper1.ps

Document Type:

text

Language:

en

Subjects:

lower bound ; exponential frame ; sine-type-function ; irregular sampling

lower bound ; exponential frame ; sine-type-function ; irregular sampling Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Growth estimates for sine-type-functions and applications to Riesz bases of exponentials

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We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive explicit lower bounds for exponential Riesz bases, as they arise in Avdonin's Theorem on 1/4 in the mean or in a Theorem of Bogmer, Ho...

We present explicit estimates for the growth of sine-type-functions as well as for the derivatives at their zero sets, thus obtaining explicit constants in a result of Levin. The estimates are then used to derive explicit lower bounds for exponential Riesz bases, as they arise in Avdonin's Theorem on 1/4 in the mean or in a Theorem of Bogmer, Horvath, Joo and Seip. An application is discussed, where knowledge of explicit lower bounds of exponential Riesz bases is desirable. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-15

Source:

http://www-m4.mathematik.tu-muenchen.de/m4/pers/lindner/lindnerpaper5.ps

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text

Language:

en

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Title:

Growth estimates for . . . applications to Riesz bases of exponentials

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-12

Source:

http://www-m4.ma.tum.de/pers/lindner/lindnerpaper5.pdf

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text

Language:

en

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Title:

Continuous time approximations to GARCH and stochastic volatility models

Publisher:

Springer

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-01-24

Source:

http://www-m4.ma.tum.de/pers/lindner/lindner5.pdf

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text

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en

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Title:

Lower bounds for finite wavelet and Gabor systems

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Given 2 L 2 (R) and a nite sequence f(a ; )g 2 R + R consisting of distinct points, the corresponding wavelet system is the set of functions f 1 a 1=2 ( x a )g 2 . We prove that for a dense set of functions 2 L 2 (R), the wavelet system corresponding to any choice of f(a ; )g 2 is linearly independent, and we derive explicite estimates for the c...

Given 2 L 2 (R) and a nite sequence f(a ; )g 2 R + R consisting of distinct points, the corresponding wavelet system is the set of functions f 1 a 1=2 ( x a )g 2 . We prove that for a dense set of functions 2 L 2 (R), the wavelet system corresponding to any choice of f(a ; )g 2 is linearly independent, and we derive explicite estimates for the corresponding lower (frame) bounds. In particular, this puts restrictions on the choice of a scaling function in the theory for multiresolution analysis. We also obtain estimates for the lower bound for Gabor systems fe 2ia x g(x )g 2 for functions g in a dense subset of L 2 (R). 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-15

Source:

http://www-m4.mathematik.tu-muenchen.de/m4/pers/lindner/lindnerpaper4.ps

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text

Language:

en

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Title:

Frames and the Feichtinger conjecture

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Abstract. We show that the conjectured generalization of the Bourgain-Tzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linear independent...

Abstract. We show that the conjectured generalization of the Bourgain-Tzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linear independent sequences. We further show that the two conjectures are implied by the paving conjecture. Finally, we show that Weyl-Heisenberg frames over rational lattices are finite unions of Riesz basic sequences. 1. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-03-24

Source:

http://www.math.ucdavis.edu/~vershynin/papers/feichtinger.pdf

http://www.math.ucdavis.edu/~vershynin/papers/feichtinger.pdf Minimize

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text

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en

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Title:

Frames and the Feichtinger conjecture

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Abstract. We show that the conjectured generalization of the Bourgain-Tzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linear independent...

Abstract. We show that the conjectured generalization of the Bourgain-Tzafriri restricted-invertibility theorem is equivalent to the conjecture of Feichtinger, stating that every bounded frame can be written as a finite union of Riesz basic sequences. We prove that any bounded frame can at least be written as a finite union of linear independent sequences. We further show that the two conjectures are implied by the paving conjecture. Finally, we show that Weyl-Heisenberg frames over rational lattices are finite unions of Riesz basic sequences. 1. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-12-23

Source:

http://www-m4.ma.tum.de/Papers/Lindner/feichtinger-conjecture.pdf

http://www-m4.ma.tum.de/Papers/Lindner/feichtinger-conjecture.pdf Minimize

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text

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en

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