The Law of Iterated Logarithm

1994 ◽  
pp. 443-460
Author(s):  
V. S. Koroljuk ◽  
Yu. V. Borovskich
Keyword(s):  
Law Of Iterated Logarithm ◽  
Iterated Logarithm ◽  
The Law

On the Law of the Iterated Logarithm for Infinite Dimensional Ornstein-Uhlenbeck Processes

1993 ◽  
Vol 45 (1) ◽  
pp. 159-175 ◽  
Author(s):  
QI-Man Shao
Keyword(s):  
Law Of Iterated Logarithm ◽  
Infinite Dimensional ◽  
Iterated Logarithm ◽  
The Law

AbstractLet be independent Ornstein-Uhlenbeck processes and In this paper the law of iterated logarithm for X(t, n)is considered. The results obtained improve those of Csorgő and Lin(1988) and Schmuland(1987).

Coronavirus Disease (COVID-19) Identification Time Analysis Using Queueing Model (Preprint)

2020 ◽  
Author(s):  
Vladimiras Dolgopolovas
Keyword(s):  
Law Of Iterated Logarithm ◽  
General Tendency ◽  
Time Analysis ◽  
Identification Process ◽  
Iterated Logarithm ◽  
Detection And Identification ◽  
In Series ◽  
Queues In Series ◽  
The Law ◽  
Evaluation Parameters

BACKGROUND The article presents an application of a model of queues in series queueing system under overloading conditions to estimate the time of detection and identification of coronavirus (COVID-19) infections. OBJECTIVE The objective is to present a simplified probabilistic model for assessing the general tendency to estimate the period of time needed to detect and identify already infected citizens before the treatment process really begins. METHODS The law of the iterated logarithm is proved for such a system, which shows that the general identification process corresponds to the law of iterated logarithm. RESULTS Some numerical examples of a different number of evaluation parameters are provided. CONCLUSIONS The modelling results showed that the sojourn time of the patient in the process of coronavirus investigation/detection/identification and treatment in the case of imbalance in the system as a whole increase in accordance with the law of the iterated logarithm. Even if the process of the treatment phases is well arranged and generally balanced, in case of the rate of investigation/detection/identification is lower than the rate of infection, the total number of already infected and unidentified citizens will increase in accordance with the law of the iterated logarithm.

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