scholarly journals A Baxter type estimator of an unknown parameter of the covariance function in the non-Gaussian case

2014 ◽  
Vol 88 ◽  
pp. 191-201
Author(s):  
O. O. Synyavs’ka
Keyword(s):  
Unknown Parameter ◽  
Covariance Function ◽  
Gaussian Case ◽  
Non Gaussian

WEAK CONVERGENCE OF NONLINEAR TRANSFORMATIONS OF INTEGRATED PROCESSES: THE MULTIVARIATE CASE

2009 ◽  
Vol 25 (5) ◽  
pp. 1180-1207 ◽  
Author(s):  
Norbert Christopeit
Keyword(s):  
Weak Convergence ◽  
Recent Work ◽  
Invariance Principle ◽  
Nonlinear Transformations ◽  
New Class ◽  
Triangular Arrays ◽  
Integrable Functions ◽  
Gaussian Case ◽  
Non Gaussian ◽  
Integrated Processes

We consider weak convergence of sample averages of nonlinearly transformed stochastic triangular arrays satisfying a functional invariance principle. A fundamental paradigm for such processes is constituted by integrated processes. The results obtained are extensions of recent work in the literature to the multivariate and non-Gaussian case. As admissible nonlinear transformation, a new class of functionals (so-called locally p-integrable functions) is introduced that adapts the concept of locally integrable functions in Pötscher (2004, Econometric Theory 20, 1–22) to the multidimensional setting.

scholarly journals Computing the Partial Correlation of ICA Models for Non-Gaussian Graph Signal Processing

Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 22 ◽  
Author(s):  
Jordi Belda ◽  
Luis Vergara ◽  
Gonzalo Safont ◽  
Addisson Salazar
Keyword(s):  
Signal Processing ◽  
Partial Correlation ◽  
Correlation Coefficients ◽  
Real Data ◽  
Linear Estimation ◽  
Precision Matrix ◽  
Conditional Mean ◽  
Graph Signal Processing ◽  
Gaussian Case ◽  
Non Gaussian

Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. The basic concept involved replacing the implicit linear estimation of conventional PCC with a nonlinear estimation (conditional mean) assuming ICA. Thus, it is better eliminated the correlation between a given pair of nodes induced by the rest of nodes, and hence the specific connectivity weights can be better estimated. Some synthetic and real data examples illustrate the approach in a graph signal processing context.

scholarly journals SMOOTH PROBABILITY MEASURES AND ASSOCIATED DIFFERENTIAL OPERATORS

1999 ◽  
Vol 02 (01) ◽  
pp. 51-78 ◽  
Author(s):  
O. G. SMOLYANOV ◽  
H. v. WEIZSÄCKER
Keyword(s):  
Differential Operators ◽  
Finite Dimensional ◽  
Differentiable Measure ◽  
Chaos Decomposition ◽  
Gaussian Case ◽  
Non Gaussian ◽  
Associated Differential Operators ◽  
Locally Convex ◽  
Nonsmooth Mappings

We compare different notions of differentiability of a measure along a vector field on a locally convex space. We consider in the L2-space of a differentiable measure the analog of the classical concepts of gradient, divergence and Laplacian (which coincides with the Ornstein–Uhlenbeck operator in the Gaussian case). We use these operators for the extension of the basic results of Malliavin and Stroock on the smoothness of finite dimensional image measures under certain nonsmooth mappings to the case of non-Gaussian measures. The proof of this extension is quite straight forward and does not use any Chaos-decomposition. Finally, the role of this Laplacian in the procedure of quantization of anharmonic oscillators is discussed.

scholarly journals Asymptotic dependence of moving average type self-similar stable random Fields

1993 ◽  
Vol 130 ◽  
pp. 85-100 ◽  
Author(s):  
Piotr S. Kokoszka ◽  
Murad S. Taqqu
Keyword(s):  
Stochastic Processes ◽  
Random Fields ◽  
Covariance Function ◽  
Moving Average ◽  
Dependence Structure ◽  
Asymptotic Dependence ◽  
Second Moments ◽  
Self Similar ◽  
Non Gaussian ◽  
Stable Random Fields

As non-Gaussian stable stochastic processes have infinite second moments, one cannot use the covariance function to describe their dependence structure.

scholarly journals Mean field approach to stochastic control with partial information

2021 ◽  
Author(s):  
Alain Bensoussan ◽  
Phillip Yam
Keyword(s):  
Partial Information ◽  
Mean Field Theory ◽  
Mean Field ◽  
Initial Distribution ◽  
Linear Quadratic ◽  
Gaussian Case ◽  
Hamilton Jacobi Bellman ◽  
Non Gaussian ◽  
Initial Distributions ◽  
Quadratic Case

In our present article, we follow our way of developing mean field type control theory in our earlier works [4], by first introducing the Bellman and then master equations, the system of Hamilton-Jacobi-Bellman (HJB) and Fokker-Planck (FP) equations, and then tackling them by looking for the semi-explicit solution for the linear quadratic case, especially with an arbitrary initial distribution; such a problem, being left open for long, has not been specifically dealt with in the earlier literature, such as [3, 13], which only tackled the linear quadratic setting with Gaussian initial distributions. Thanks to the effective mean-field theory, we propose a solution to this long standing problem of the general non-Gaussian case. Besides, our problem considered here can be reduced to the model in [2], which is fundamentally different from our present proposed framework.

scholarly journals CORRELATORS OF THE KAZAKOV-MIGDAL MODEL

1993 ◽  
Vol 08 (25) ◽  
pp. 2387-2401 ◽  
Author(s):  
M. I. DOBROLIUBOV ◽  
YU. MAKEENKO ◽  
G. W. SEMENOFF
Keyword(s):  
Matrix Model ◽  
Explicit Solution ◽  
Scalar Fields ◽  
Algebraic Equations ◽  
Quadratic Potential ◽  
Large N ◽  
Gaussian Case ◽  
The One ◽  
Non Gaussian

We derive loop equations for the one-link correlators of gauge and scalar fields in the Kazakov-Migdal model. These equations determine the solution of the model in the large-N limit and are similar to analogous equations for the Hermitian two-matrix model. We give an explicit solution of the equations for the case of a Gaussian, quadratic potential. We also show how similar calculations in a non-Gaussian case reduce to purely algebraic equations.

scholarly journals UNIFIED DESCRIPTION OF CORRELATORS IN NON-GAUSSIAN PHASES OF HERMITIAN MATRIX MODEL

2006 ◽  
Vol 21 (12) ◽  
pp. 2481-2517 ◽  
Author(s):  
A. ALEXANDROV ◽  
A. MIRONOV ◽  
A. MOROZOV
Keyword(s):  
Matrix Model ◽  
Hermitian Matrix ◽  
Partition Functions ◽  
Unified Approach ◽  
Small Space ◽  
Linear Differential ◽  
Gaussian Case ◽  
Non Gaussian ◽  
Hermitian Matrix Model ◽  
Unified Description

Following the program, proposed in hep-th/0310113, of systematizing known properties of matrix model partition functions (defined as solutions to the Virasoro-like sets of linear differential equations), we proceed to consideration of non-Gaussian phases of the Hermitian one-matrix model. A unified approach is proposed for description of "connected correlators" in the form of the phase-independent "check-operators" acting on the small space of T-variables (which parametrize the polynomial W(z)). With appropriate definitions and ordering prescriptions, the multidensity check-operators look very similar to the Gaussian case (however, a reliable proof of suggested explicit expressions in all loops is not yet available, only certain consistency checks are performed).

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