Atsitiktinio skaičiaus dvimačių vektorių maksimumų konvergavimo greičio įvertis

Nonlinearly normalized maxima of independent and identically distributed random vectors are pre-sented in this work. We’ve obtained nonuniform estimate of convergence in transfer theorem in case when normalization is nonlinear.  Šiame darbe nagrinėjame netiesiškai normalizuotų dvimačių atsitiktinio skai-čiaus vektorių maksimumų struktūrą. Gauname šios struktūros konvergavimo greičio įverčio išraišką perkėlimo teoremoje. Šiame straipsnyje apibendriname rezultatus, gautus [2] darbe. &nbsp

A note on the tail behavior of randomly weighted and stopped dependent sums

In this paper, we deal with the tail behavior of the maximum of randomly weighted and stopped sums. We assume that primary random variables (with a certain dependence structure) are identically distributed with heavy-tailed distribution function and random weights are nonnegative. In this note, we specify some conditions for the (weak) asymptotics of the tail of random maximum

Sunkiauodegių atsitiktinių dydžių sumų asimptotinė analizė

In the thesis the sums of dependent nonidentically distributed heavy-tailed random variables are investigated. With some conditions for the (heavy-tailed) distribution of maximal element, the weak max-sum equivalence is proved. Some copula-based examples of dependence structures are given. The sums with dependent nonidentically distributed r.v.s and positive random weights are discussed. The closure property of weighted sums is proved. That is, given that marginal distributions are from the long-tailed distribution class, the distribution of sum belongs to the same class. Moreover, asymptotic equivalence of the tail probabilities of the sum and the sum of nonnegative random variables with their weights is shown. It is shown that this result holds if dependence of random variables is generated by the well-known FGM copula. Finally, the randomly weighted and stopped dependent sums with identically distributed dependent heavy-tailed r.v.s are discussed. The asymptotic lower and upper bounds for the tail distributions of maximum of such randomly stopped sums are derived. Furthermore, the conditions for this result are shown for the wide class of heavy tailed distribution functions and dependence structures

Asymptotic analysis of the sums of heavy-tailed random variables

In this summary the main results of the dissertation are presented. In the thesis the sums of dependent nonidentically distributed heavy-tailed random variables are investigated. With some conditions for the (heavy-tailed) distribution of maximal element, the weak max-sum equivalence is proved. Some copula-based examples of dependence structures are given. The sums with dependent nonidentically distributed r.v.s and positive random weights are discussed. The closure property of weighted sums is proved. That is, given that marginal distributions are from the long-tailed distribution class, the distribution of sum belongs to the same class. Moreover, asymptotic equivalence of the tail probabilities of the sum and the sum of nonnegative random variables with their weights is shown. It is shown that this result holds if dependence of random variables X1,...,Xn is generated by the well-known FGM copula. Finally, the randomly weighted and stopped dependent sums with identically distributed dependent heavy-tailed r.v.s X1,...,Xn are discussed. The asymptotic lower and upper bounds for the tail distributions of maximum of such randomly stopped sums are derived. Furthermore, the conditions for this result are shown for the wide class of heavy tailed distribution functions and dependence structures

Atsitiktinio skaičiaus vektorių maksimumų konvergavimo greičio įvertis

Linearly normalized maxima of independent and identically distributed random vectors is presented in this work. We’ve obtained nonuniform estimate of convergence in case when normalization is linear. For clearness there is given an example is this paper. Transfer theorem was aplied.Šiame darbe nagrinėjame tiesiškai normalizuotų dvimačių atsitiktinio skaičiaus vektorių maksimumų struktūrą. Taikome perkėlimo teoremą, kurios pagalba gauname šios struktūros konvergavimo greičio įverčio išraišką. Pateikiame pavyzdį, iliustruojantį teorinę medžiagą. Šiame straipsnyje patikslinsime rezultatus, gautus [1] darbe

Perfectly secure Shannon cipher construction based on the matrix power function

A Shannon cipher can be used as a building block for the block cipher construction if it is considered as one data block cipher. It has been proved that a Shannon cipher based on a matrix power function (MPF) is perfectly secure. This property was obtained by the special selection of algebraic structures to define the MPF. In an earlier paper we demonstrated, that certain MPF can be treated as a conjectured one-way function. This property is important since finding the inverse of a one-way function is related to an NP-complete problem. The obtained results of perfect security on a theoretical level coincide with the NP-completeness notion due to the well known Yao theorem. The proposed cipher does not need multiple rounds for the encryption of one data block and hence can be effectively parallelized since operations with matrices allow this effective parallelization

Association of hair cortisol concentration with prevalence of major cardiovascular risk factors and allostatic load

Abstract BACKGROUND The high prevalence of cardiovascular diseases cannot be explained completely by conventional risk factors such as older age, smoking, diabetes mellitus, hypertension, obesity, and dyslipidemia. Results of recent studies indicate that chronic stress may be an independent risk factor for cardiovascular morbidity and mortality. Thus, the aim of our study was to investigate the associations between the hair cortisol concentration (HCC), which is considered as a potential biomarker of long-term psychosocial stress, and traditional cardiovascular risk factors, including smoking, dyslipidemia, hypertension, and obesity. MATERIAL AND METHODS Fasting blood samples and anthropometric and lifestyle data were collected from 163 apparently healthy men. HCC was determined using high-performance liquid chromatography. Allostatic load (AL) index, defined as an integrated score of multiple interacting systems involved in the adaptation to adverse physical or psychosocial situations, was also calculated. RESULTS We found that many prevalent cardiovascular risk factors, including hypertension, smoking, higher than recommended waist circumference (WC), and low-density lipoprotein cholesterol (LDL-C) median values, are associated with higher HCC. Hair cortisol level was also positively associated with the manifestation of individual cardiovascular risk factors such as higher-than-recommended total cholesterol, LDL-C, non-high-density lipoprotein cholesterol, body mass index, and WC median values. Moreover, a significant positive relationship between HCC and AL index was observed. CONCLUSIONS The results of this study suggest that increased prevalence of traditional cardiovascular risk factors is associated with higher HCC. Also, both HCC and AL index might be appropriate markers for the evaluation of chronic stress level