A Gaussian Inequality for Expected Absolute Products

Li, Wenbo V.; Wei, Ang

doi:10.1007/s10959-010-0329-0

Cited by 38 publications

(29 citation statements)

References 16 publications

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“…Malicet et al [14]) that the Gaussian product conjecture (1.1) is a sufficient condition for the 'real linear polarization constant' problem, which was raised by Benítem, Sarantopolous and Tonge [3] and is still unsolved. In [13], Li and Wei proposed the following improved version of the Gaussian product conjecture:…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

The three-dimensional Gaussian product inequality

Lan

Sun

2020

Journal of Mathematical Analysis and Applications

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We prove the 3-dimensional Gaussian product inequality, i.e., for any real-valued centered Gaussian random vector (X, Y, Z) and m ∈ N, it holds thatOur proof is based on some improved inequalities on multi-term products involving 2-dimensional Gaussian random vectors. The improved inequalities are derived using the Gaussian hypergeometric functions and have independent interest. As by-products, several new combinatorial identities and inequalities are obtained. MSC: Primary 60E15; Secondary 62H12

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Section: Introduction and Main Resultsmentioning

confidence: 99%

The three-dimensional Gaussian product inequality

Lan

Sun

2020

Journal of Mathematical Analysis and Applications

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“…Furthermore, let (X t ) t∈[0,T ] be the weak solution of (3). Consider the approximating sequence of strong solutions {(X d,ε t ) t∈[0,T ] } d≥1,ε>0 of SDEs (24), where b d,ε : [0, T ]×H → H is defined as in (26). Then, for every t ∈ [0, T ] and for any bounded continuous function φ :…”

Section: Definition 42mentioning

confidence: 99%

Restoration of Well-Posedness of Infinite-dimensional Singular ODE's via Noise

Baños¹,

Bauer²,

Meyer‐Brandis³

et al. 2019

Preprint

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In this paper we aim at generalizing the results of A. K. Zvonkin [41] and A. Y. Veretennikov [39] on the construction of unique strong solutions of stochastic differential equations with singular drift vector field and additive noise in the Euclidean space to the case of infinite-dimensional state spaces. The regularizing driving noise in our equation is chosen to be a locally non-Hölder continuous Hilbert space valued process of fractal nature, which does not allow for the use of classical construction techniques for strong solutions from PDE or semimartingale theory. Our approach, which does not resort to the Yamada-Watanabe principle for the verification of pathwise uniqueness of solutions, is based on Malliavin calculus.

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“…where the c ij 's are constant. Further, the expectations of the absolute values of the components are finite since E[|xx T | ij ] < ∞ (Li and Wei, 2012). Now let…”

Section: Simple Casementioning

confidence: 99%

“…To build a model for equilibrium data, first consider a first-order vector autoregres- sive, or VAR(1) model for time-series data for a system with p genes with no correlation in the error term between genes (Lütkepohl, 2005). We can write the model as where boldD is diagonal, boldxt and boldεt are vectors of length p, while boldA and boldD are p×p matrices.…”

Section: First-order Vector Autoregressive Modelmentioning

confidence: 99%

Identifying dynamical time series model parameters from equilibrium samples, with application to gene regulatory networks

Young

Yeung

Raftery

2018

Statistical Modelling

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Gene regulatory network reconstruction is an essential task of genomics in order to further our understanding of how genes interact dynamically with each other. The most readily available data, however, are from steady-state observations. These data are not as informative about the relational dynamics between genes as knockout or over-expression experiments, which attempt to control the expression of individual genes. We develop a new framework for network inference using samples from the equilibrium distribution of a vector autoregressive (VAR) time-series model which can be applied to steady-state gene expression data. We explore the theoretical aspects of our method and apply the method to synthetic gene expression data generated using GeneNetWeaver.

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A Gaussian Inequality for Expected Absolute Products

Cited by 38 publications

References 16 publications

The three-dimensional Gaussian product inequality

The three-dimensional Gaussian product inequality

Restoration of Well-Posedness of Infinite-dimensional Singular ODE's via Noise

Identifying dynamical time series model parameters from equilibrium samples, with application to gene regulatory networks

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