A limit theorem for stochastic functions, constructed in terms of quadratic forms from Gaussian random variables

1989 ◽  
Vol 40 (4) ◽  
pp. 419-424
Author(s):  
Yu. M. Ryzhov
Keyword(s):  
Limit Theorem ◽  
Quadratic Forms ◽  
Random Variables ◽  
Gaussian Random Variables ◽  
Stochastic Functions

On Distribution of Quadratic Forms in Gaussian Random Variables

1996 ◽  
Vol 40 (2) ◽  
pp. 250-260 ◽  
Author(s):  
G. Christoph ◽  
Yu. V. Prokhorov ◽  
V. V. Ulyanov
Keyword(s):  
Quadratic Forms ◽  
Random Variables ◽  
Gaussian Random Variables

scholarly journals On the Distribution of Indefinite Quadratic Forms in Gaussian Random Variables

2016 ◽  
Vol 64 (1) ◽  
pp. 153-165 ◽  
Author(s):  
Tareq Y. Al-Naffouri ◽  
Muhammed Moinuddin ◽  
Nizar Ajeeb ◽  
Babak Hassibi ◽  
Aris L. Moustakas
Keyword(s):  
Quadratic Forms ◽  
Random Variables ◽  
Gaussian Random Variables ◽  
Indefinite Quadratic

scholarly journals Two Properties of Vectors of Quadratic Forms in Gaussian Random Variables

2015 ◽  
Vol 59 (2) ◽  
pp. 208-221 ◽  
Author(s):  
V. I. Bogachev ◽  
E. D. Kosov ◽  
I. Nourdin ◽  
G. Poly
Keyword(s):  
Quadratic Forms ◽  
Random Variables ◽  
Gaussian Random Variables

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

scholarly journals A counterexample to the existence of a general central limit theorem for pairwise independent identically distributed random variables

2021 ◽  
Vol 499 (1) ◽  
pp. 124982
Author(s):  
Benjamin Avanzi ◽  
Guillaume Boglioni Beaulieu ◽  
Pierre Lafaye de Micheaux ◽  
Frédéric Ouimet ◽  
Bernard Wong
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Independent Identically Distributed
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