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Set of Gaussian Random Variables
"... Abstract—This paper quantifies the approximation error when results obtained by Clark (Oper. Res., vol. 9, p. 145, 1961) are employed to compute the maximum (max) of Gaussian random variables, which is a fundamental operation in statistical timing. We show that a finite lookup table can be used to s ..."
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Abstract—This paper quantifies the approximation error when results obtained by Clark (Oper. Res., vol. 9, p. 145, 1961) are employed to compute the maximum (max) of Gaussian random variables, which is a fundamental operation in statistical timing. We show that a finite lookup table can be used
On the structure of Gaussian random variables
, 2009
"... We study when a given Gaussian random variable on a given probability space (Ω, F, P) is equal almost surely to β1 where β is a Brownian motion defined on the same (or possibly extended) probability space. As a consequence of this result, we prove that the distribution of a random variable in a fini ..."
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Cited by 2 (2 self)
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We study when a given Gaussian random variable on a given probability space (Ω, F, P) is equal almost surely to β1 where β is a Brownian motion defined on the same (or possibly extended) probability space. As a consequence of this result, we prove that the distribution of a random variable in a
Estimation of NonGaussian Random Variables in Gaussian Noise
 Properties of the MMSE” 2008 IEEE Int. Symposium on Information Theory
"... Abstract—This work studies the properties of the minimum meansquare error (MMSE) of estimating an arbitrary random variable contaminated by Gaussian noise based on the observation. The MMSE can be regarded as a function of the signaltonoise ratio (SNR), as well as a functional or transform of th ..."
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Cited by 12 (5 self)
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Abstract—This work studies the properties of the minimum meansquare error (MMSE) of estimating an arbitrary random variable contaminated by Gaussian noise based on the observation. The MMSE can be regarded as a function of the signaltonoise ratio (SNR), as well as a functional or transform
1AN EXTREMAL INEQUALITY RELATED TO HYPERCONTRACTIVITY OF GAUSSIAN RANDOM VARIABLES
"... We establish that Gaussian distributions are the optimizers for a particular optimization problem related to determining the hypercontractivity parameters for a pair of jointly Gaussian random variables. 1. ..."
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We establish that Gaussian distributions are the optimizers for a particular optimization problem related to determining the hypercontractivity parameters for a pair of jointly Gaussian random variables. 1.
Two properties of vectors of quadratic forms in Gaussian random variables
"... Abstract: We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some interesting consequences. Our second result gives a char ..."
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Abstract: We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some interesting consequences. Our second result gives a
1.4. Gaussian Random Variables 6
"... Abstract. The aim of this text is to give an introduction to Ito ̂ calculus. It is based on a short course about the subject given by the author at the WKSummer camp 2006 at the lake Weissensee in Austria. The emphasis lies on the probabilistic basics of the stochastic integration and, in the secon ..."
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Abstract. The aim of this text is to give an introduction to Ito ̂ calculus. It is based on a short course about the subject given by the author at the WKSummer camp 2006 at the lake Weissensee in Austria. The emphasis lies on the probabilistic basics of the stochastic integration and, in the second part,
ESTIMATION OF WIENER–ITÔ INTEGRALS AND POLYNOMIALS OF INDEPENDENT GAUSSIAN RANDOM VARIABLES.
, 803
"... In this paper I prove good estimates on the moments and tail distribution of kfold Wiener–Itô integrals and also present their natural counterpart for polynomials of independent Gaussian random variables. The proof is based on the socalled diagram formula for Wiener–Itô integrals which yields a go ..."
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In this paper I prove good estimates on the moments and tail distribution of kfold Wiener–Itô integrals and also present their natural counterpart for polynomials of independent Gaussian random variables. The proof is based on the socalled diagram formula for Wiener–Itô integrals which yields a
Most notes are based on Chapter IVB and Chapter V of Poor’s Introduction to Signal Detection and Estimation book [1]. 1 Jointly Gaussian random variables
, 2012
"... Jointly Gaussian random variables, MMSE and linear ..."
CORRELATION INEQUALITIES AND APPLICATIONS TO VECTORVALUED GAUSSIAN RANDOM VARIABLES AND FRACTIONAL BROWNIAN MOTION
"... Abstract. In this paper we extend certain correlation inequalities for vectorvalued Gaussian random variables due to Kolmogorov and Rozanov. The inequalities are applied to sequences of Gaussian random variables and Gaussian processes. For sequences of Gaussian random variables satisfying a correl ..."
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Abstract. In this paper we extend certain correlation inequalities for vectorvalued Gaussian random variables due to Kolmogorov and Rozanov. The inequalities are applied to sequences of Gaussian random variables and Gaussian processes. For sequences of Gaussian random variables satisfying a
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