scholarly journals Fourth moment theorems on the Poisson space: analytic statements via product formulae

2018 ◽  
Vol 23 ◽  
Author(s):  
Christian Döbler ◽  
Giovanni Peccati
Keyword(s):  
Fourth Moment ◽  
Poisson Space

scholarly journals The fourth moment theorem on the Poisson space

2018 ◽  
Vol 46 (4) ◽  
pp. 1878-1916 ◽  
Author(s):  
Christian Döbler ◽  
Giovanni Peccati
Keyword(s):  
Fourth Moment ◽  
Poisson Space

scholarly journals Fourth moment theorems on the Poisson space in any dimension

2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Christian Döbler ◽  
Anna Vidotto ◽  
Guangqu Zheng
Keyword(s):  
Fourth Moment ◽  
Poisson Space

The Poisson space cPX for Δu = cu with rotation-free c

1978 ◽  
Vol 64 (1) ◽  
pp. 651-658 ◽  
Author(s):  
Abderrahman Boukricha ◽  
Hermann Hueber
Keyword(s):  
Poisson Space

The fourth moment of Ramanujan ?-function

1983 ◽  
Vol 266 (2) ◽  
pp. 233-239 ◽  
Author(s):  
Carlos J. Moreno ◽  
Freydoon Shahidi
Keyword(s):  
Fourth Moment

scholarly journals Exact tensor closures for the three-dimensional Jeffery's equation

2011 ◽  
Vol 680 ◽  
pp. 321-335 ◽  
Author(s):  
STEPHEN MONTGOMERY-SMITH ◽  
WEI HE ◽  
DAVID A. JACK ◽  
DOUGLAS E. SMITH
Keyword(s):  
Fibre Orientation ◽  
Elliptic Integral ◽  
Moment Tensor ◽  
Three Dimensional ◽  
Exact Formula ◽  
Fourth Moment ◽  
Newtonian Flow ◽  
Curve Fit ◽  
Explicit Formulae ◽  
Jeffery’S Equation

This paper presents an exact formula for calculating the fourth-moment tensor from the second-moment tensor for the three-dimensional Jeffery's equation. Although this approach falls within the category of a moment tensor closure, it does not rely upon an approximation, either analytic or curve fit, of the fourth-moment tensor as do previous closures. This closure is orthotropic in the sense of Cintra & Tucker (J. Rheol., vol. 39, 1995, p. 1095), or equivalently, a natural closure in the sense of Verleye & Dupret (Developments in Non-Newtonian Flow, 1993, p. 139). The existence of these explicit formulae has been asserted previously, but as far as the authors know, the explicit forms have yet to be published. The formulae involve elliptic integrals, and are valid whenever fibre orientation was isotropic at some point in time. Finally, this paper presents the fast exact closure, a fast and in principle exact method for solving Jeffery's equation, which does not require approximate closures nor the elliptic integral computation.

Fourth Moment Structure of Markov Switching Multivariate GARCH Models

2019 ◽  
Author(s):  
Maddalena Cavicchioli
Keyword(s):  
Closed Form ◽  
Moving Average ◽  
Markov Switching ◽  
Computational Cost ◽  
Sufficient Conditions ◽  
Impulse Response Function ◽  
Real Data ◽  
Multivariate Garch ◽  
Fourth Moment ◽  
Spectral Density Matrix

Abstract We derive sufficient conditions for the existence of second and fourth moments of Markov switching multivariate generalized autoregressive conditional heteroscedastic processes in the general vector specification. We provide matrix expressions in closed form for such moments, which are obtained by using a Markov switching vector autoregressive moving-average representation of the initial process. These expressions are shown to be readily programmable in addition of greatly reducing the computational cost. As theoretical applications of the results, we derive the spectral density matrix of the squares and cross products, propose a new definition of multivariate kurtosis measure to recognize heavy-tailed features in financial real data, and provide a matrix expression in closed form of the impulse-response function for the volatility. An empirical example illustrates the results.

An inverse scattering method in time-domain electromagnetics

1981 ◽  
Vol 59 (10) ◽  
pp. 1348-1353
Author(s):  
Sujeet K. Chaudhuri
Keyword(s):  
Inverse Scattering ◽  
Time Domain ◽  
Random Noise ◽  
Power Series Expansion ◽  
Inverse Scattering Method ◽  
Wave Number ◽  
Moment Condition ◽  
Scattering Method ◽  
Fourth Moment ◽  
Rayleigh Coefficient

An inverse scattering model, based on the time-domain concepts of electromagnetic theory is developed. Using the first five (zeroth to fourth) moment condition integrals, the Rayleigh coefficient and the next higher order nonzero coefficient of the power series expansion in k (wave number) of the object backscattering response are recovered. The Rayleigh coefficient and the other coefficient thus recovered are used (with the ellipsoidal assumption for the object shape) to determine the dimensions and orientation of the object.Some numerical results of the application of this coefficient recovery technique to conducting ellipsoidal scatterers are presented. The performance of the software system in the presence of normally distributed random noise is also studied.

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