Cox limit theorem for large excursions of a norm of a Gaussian vector process

2010 ◽  
Vol 80 (19-20) ◽  
pp. 1479-1485 ◽  
Author(s):  
Biljana Stamatovic ◽  
Sinisa Stamatovic
Keyword(s):  
Limit Theorem ◽  
Gaussian Vector ◽  
Vector Process

The almost sure limit theorem for the maxima and minima of strongly dependent Gaussian vector sequences

Extremes ◽  
2011 ◽  
Vol 15 (3) ◽  
pp. 389-406 ◽  
Author(s):  
Zhichao Weng ◽  
Zuoxiang Peng ◽  
Saralees Nadarajah
Keyword(s):  
Limit Theorem ◽  
Gaussian Vector ◽  
Almost Sure Limit Theorem ◽  
Vector Sequences

Simulating a non-Gaussian vector process with application in hydrology

2014 ◽  
Vol 41 (6) ◽  
pp. 621-626 ◽  
Author(s):  
A. V. Frolov ◽  
T. Yu. Vyruchalkina ◽  
I. V. Solomonova
Keyword(s):  
Gaussian Vector ◽  
Vector Process ◽  
Non Gaussian

scholarly journals High excursions of Bessel process and other processes of Bessel type

2019 ◽  
Vol 487 (3) ◽  
pp. 238-241
Author(s):  
V. I. Piterbarg ◽  
I. V. Rodionov
Keyword(s):  
Single Point ◽  
Bessel Process ◽  
Absolute Maximum ◽  
Time Interval ◽  
Gaussian Vector ◽  
Vector Process ◽  
Distributed Components ◽  
Excursion Probability ◽  
Independent Identically Distributed

A high excursion probability for the modulus of a Gaussian vector process with independent identically distributed components is evaluated. It is assumed that the components have means zero and variances reaching its absolute maximum at a single point of the considered time interval. An important example of such processes is the Bessel process.

scholarly journals A central limit theorem for systems of regressions

1961 ◽  
Vol 57 (3) ◽  
pp. 583-588 ◽  
Author(s):  
E. J. Hannan
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Harmonic Analysis ◽  
Central Limit ◽  
Linear Process ◽  
Regression Coefficients ◽  
Vector Process

ABSTRACTA central limit theorem is proved for the estimates of the regression coefficients in a multiple system of regressions when the vector process generating the residuals is a linear process with coefficient matrices the sum of whose norms converges. The regressor variables are assumed to satisfy conditions, due to Grenander, which make their generalized harmonic analysis possible.

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