The Law of the Iterated Logarithm for Linear Processes Generated by a Sequence of Stationary Independent Random Variables under the Sub-Linear Expectation

In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive capacity.

The Law of the Iterated Logarithm for Random Dynamical System with Jumps and State-Dependent Jump Intensity

In this paper our considerations are focused on some Markov chain associated with certain piecewise-deterministic Markov process with a state-dependent jump intensity for which the exponential ergodicity was obtained in [4]. Using the results from [3] we show that the law of iterated logarithm holds for such a model.

The law of iterated logarithm for a class of random variables satisfying Rosenthal type inequality

<abstract><p>Let $ \{Y_n, n\geq 1\} $ be sequence of random variables with $ EY_n = 0 $ and $ \sup_nE|Y_n|^p &lt; \infty $ for each $ p &gt; 2 $ satisfying Rosenthal type inequality. In this paper, the law of the iterated logarithm for a class of random variable sequence with non-identical distributions is established by the Rosenthal type inequality and Berry-Esseen bounds. The results extend the known ones from i.i.d and NA cases to a class of random variable satisfying Rosenthal type inequality.</p></abstract>

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

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.