Branching processes in random environment die slowly

Let $Z_{n,}n=0,1,...,$ be a branching process evolving in the random environment generated by a sequence of iid generating functions $f_{0}(s),f_{1}(s),...,$ and let $S_{0}=0,S_{k}=X_{1}+...+X_{k},k\geq 1,$ be the associated random walk with $X_{i}=\log f_{i-1}^{\prime}(1),$ $\tau (m,n)$ be the left-most point of minimum of $\left\{S_{k},k\geq 0\right\}$ on the interval $[m,n],$ and $T=\min \left\{k:Z_{k}=0\right\}$. Assuming that the associated random walk satisfies the Doney condition $P(S_{n}>0) \to \rho \in (0,1),n\to \infty ,$ we prove (under the quenched approach) conditional limit theorems, as $n\to \infty$, for the distribution of $Z_{nt},$ $Z_{\tau (0,nt)},$ and $Z_{\tau (nt,n)},$ $t\in (0,1),$ given $T=n$. It is shown that the form of the limit distributions essentially depends on the location of $\tau (0,n)$ with respect to the point $nt.

Criticality for branching processes in random environment

We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching processes are developed under a general assumption, known as Spitzer's condition in fluctuation theory of random walks, and some additional moment condition. We determine the exact asymptotic behavior of the survival probability and prove conditional functional limit theorems for the generation size process and the associated random walk. The results rely on a stimulating interplay between branching process theory and fluctuation theory of random walks.Comment: Published at http://dx.doi.org/10.1214/009117904000000928 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

PREVALENCE OF ARTERIAL HYPERTENSION AND RISK FACTORS IN YOUNG ADULTS

Arterial hypertension (AH) is one of the most widespread diseases in whole the world. AH in youth is associated with high cardiovascular mortality in middle age.Objectives: The study objectives were to studied prevalence of AH and risk factors in young adults.Methods. We studied prevalence of AH and risk factors in 981 young adults aged 20-29 years old (22,3 ± 2,26) in cross-sectional epidemiological study.Results. Prevalence of AH was 14,2%, it was significantly higher in men (22,2%) then in women (4,5%), p>0,05. There was a high prevalence of AH risk factors: overweight (35,4% in men), smoking (27,8% in men), parental hypertension (57,8%), noncompliance of day regimen (58,8%), high stress level (37,7%). In AH group prevalence of overweight, smoking, high salt consumption, parental hypertension and hypodinamia was significantly higher than in population.Conclusions. Prevalence of AH was 14,2%, main risk factors of AH were observed in more then quarter of studied persons

Evolutionary branching in a stochastic population model with discrete mutational steps

Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a trait, and also by population sizes, and that mutations lead to small changes in trait value. Then, traditionally, the evolutionary dynamics is studied in the limit of vanishing mutational step sizes. In the present approach, small but non-negligible mutational steps are considered. By means of theoretical analysis in the limit of infinitely large populations, as well as computer simulations, we demonstrate how discrete mutational steps affect the patterns of evolutionary branching. We also argue that the average time to the first branching depends in a sensitive way on both mutational step size and population size.Comment: 12 pages, 8 figures. Revised versio