A Non-Classical Estimate of the Speed of Convergence in the Multidimensional Central Limit Theorem Taking into Account Large Deviations

1979 ◽  
Vol 23 (3) ◽  
pp. 667-671 ◽  
Author(s):  
S. Ya. Shorgin
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Large Deviations ◽  
Central Limit ◽  
Speed Of Convergence ◽  
Multidimensional Central Limit Theorem ◽  
Classical Estimate

scholarly journals On the estimation of the remainder term in the multidimensional central limit theorem

1971 ◽  
Vol 11 (4) ◽  
pp. 905-910
Author(s):  
H. Jasiūnas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Multidimensional Central Limit Theorem

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Г. Ясюнас. Об оценке остаточного члена в многомерной центральной предельной теореме H. Jasiūnas. Liekamoje nario įvertinimas daugiamatėje centrinėje ribinėje teoremoje

On the behaviour of a long cascade of linear reservoirs

2000 ◽  
Vol 37 (02) ◽  
pp. 417-428
Author(s):  
John E. Glynn ◽  
Peter W. Glynn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Large Deviations ◽  
Asymptotic Behaviour ◽  
Central Limit ◽  
Tail Probabilities ◽  
Logarithmic Asymptotics ◽  
Random Fluctuations

This paper describes the limiting asymptotic behaviour of a long cascade of linear reservoirs fed by stationary inflows into the first reservoir. We show that the storage in the nth reservoir becomes asymptotically deterministic as n → ∞, and establish a central limit theorem for the random fluctuations about the deterministic approximation. In addition, we prove a large deviations theorem that provides precise logarithmic asymptotics for the tail probabilities associated with the storage in the nth reservoir when n is large.

On the behaviour of a long cascade of linear reservoirs

2000 ◽  
Vol 37 (2) ◽  
pp. 417-428
Author(s):  
John E. Glynn ◽  
Peter W. Glynn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Large Deviations ◽  
Asymptotic Behaviour ◽  
Central Limit ◽  
Tail Probabilities ◽  
Logarithmic Asymptotics ◽  
Random Fluctuations

This paper describes the limiting asymptotic behaviour of a long cascade of linear reservoirs fed by stationary inflows into the first reservoir. We show that the storage in the nth reservoir becomes asymptotically deterministic as n → ∞, and establish a central limit theorem for the random fluctuations about the deterministic approximation. In addition, we prove a large deviations theorem that provides precise logarithmic asymptotics for the tail probabilities associated with the storage in the nth reservoir when n is large.

Sign in / Sign up

Export Citation Format

Share Document