Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Case of Long-Range Dependence

Functional central limit theorem; Occupation time uctuation; Branching particle system; Distribution-valued Gaussian process; Fractional Brownian motion; Sub-fractional Brownian motion; Long-range dependence

A Long Range Dependence Stable Process and an Infinite Variance Branching System

We prove a functional limit theorem for the rescaled occupation time fluctuations of a (d, , )- branching particle system (particles moving in Rd according to a symmetric -stable L´evy process, branching law in the domain of attraction of a (1 + )-stable law, 0 d/(d + ), which coincides with the case of finite variance branching ( = 1), and another one for d/(d + ), where the long range dependence depends on the value of . The long range dependence is characterized by a dependence exponent which describes the asymptotic behavior of the codierence of increments of on intervals far apart, and which is d/ for the first case and (1 + - d/(d + ))d/ for the second one. The convergence proofs use techniques of S0(Rd)-valued processes.Branching particle system, occupation time fluctuation, functional limit theorem, stable process, long range dependence.

Occupation Time Fluctuations of an Infinite Variance Branching System in Large Dimensions

We prove limit theorems for rescaled occupation time fluctuations of a (d, , )-branching particle system (particles moving in Rd according to a spherically symmetric -stable L´evy process, (1 + )- branching, 0 (1 + )/. The fluctuation processes are continuous but their limits are stable processes with independent increments, which have jumps. The convergence is in the sense of finite-dimensional distributions, and also of space-time random fields (tightness does not hold in the usual Skorohod topology). The results are in sharp contrast with those for intermediate dimensions, /Branching particle system, critical and large dimensions, limit theorem, occupation time fluctuation, stable process.

Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Cases of Large and Critical Dimensions

Functional central limit theorem; Occupation time fluctuation; Branching particle system; Generalized Wiener process; Critical dimension

Occupation time limits of inhomogeneous Poisson systems of independent particles

We prove functional limits theorems for the occupation time process of a system of particles moving independently in $R^d$ according to a symmetric $\alpha$-stable L\'evy process, and starting off from an inhomogeneous Poisson point measure with intensity measure $\mu(dx)=(1+|x|^{\gamma})^{-1}dx,\gamma>0$, and other related measures. In contrast to the homogeneous case $(\gamma=0)$, the system is not in equilibrium and ultimately it vanishes, and there are more different types of occupation time limit processes depending on arrangements of the parameters $\gamma, d$ and $\alpha$. The case $\gamma<d<\alpha$ leads to an extension of fractional Brownian motion.Comment: 22 page

Oscillatory Fractional Brownian Motion and Hierarchical Random Walks

We introduce oscillatory analogues of fractional Brownian motion, sub-fractional Brownian motion and other related long range dependent Gaussian processes, we discuss their properties, and we show how they arise from particle systems with or without branching and with different types of initial conditions, where the individual particle motion is the so-called c-random walk on a hierarchical group. The oscillations are caused by the discrete and ultrametric structure of the hierarchical group, and they become slower as time tends to infinity and faster as time approaches zero. We also give other results to provide an overall picture of the behavior of this kind of systems, emphasizing the new phenomena that are caused by the ultrametric structure as compared with results for analogous models on Euclidean space

The Effectiveness of Family Constellation Therapy in Improving Mental Health:A Systematic ReviewPalabras clave(sic)(sic)(sic)

Family/systemic constellation therapy is a short-term group intervention aiming to help clients better understand and then change their conflictive experiences within a social system (e.g., family). The aim of the present systematic review was to synthetize the empirical evidence on the tolerability and effectiveness of this intervention in improving mental health. The PsycINFO, Embase, MEDLINE, ISI Web of Science, Psyndex, PsycEXTRA, ProQuest Dissertations & Theses, The Cochrane Library, Google Scholar, and an intervention-specific organization's databases were searched for quantitative, prospective studies published in English, German, Spanish, French, Dutch or Hungarian up until April 2020. Out of 4,197 identified records, 67 were assessed for eligibility, with 12 studies fulfilling inclusion criteria (10 independent samples; altogether 568 participants). Outcome variables were diverse ranging from positive self-image through psychopathology to perceived quality of family relationships. Out of the 12 studies, nine showed statistically significant improvement postintervention. The studies showing no significant treatment benefit were of lower methodological quality. The random-effect meta-analysis-conducted on five studies in relation to general psychopathology-indicated a moderate effect (Hedges' g of 0.531, CI: 0.387-0.676). Authors of seven studies also investigated potential iatrogenic effects and four studies reported minor or moderate negative effects in a small proportion (5-8%) of participants that potentially could have been linked to the intervention. The data accumulated to date point into the direction that family constellation therapy is an effective intervention with significant mental health benefits in the general population; however, the quantity and overall quality of the evidence is low

The Forest Data Bank in Poland as compared with databases and information sharing systems in forestry in other countries

W opracowaniu dokonano charakterystyki rodzajów baz danych i systemów udostępniania informacji z zakresu leśnictwa na poziomie globalnym oraz w różnych krajach. Przeanalizowano ich zawartość i dostępne funkcjonalności. Na tym tle opisano polski Bank Danych o Lasach (BDL): jego główne zadania, zasób informacyjny i rozwiązania techniczne służące do udostępniania danych. Przeanalizowano aktualny stan gromadzenia i udostępniania informacji o lasach na świecie oraz uwarunkowania rozwoju w tym zakresie. Szczególną uwagę zwrócono na BDL, który w porównaniu z innymi bazami danych na poziomie krajowym jest jednym z bogatszych i bardziej kompletnych źródeł informacji o lasach.The study characterizes types of databases and information sharing systems in forestry at the global level and in various countries. We have presented their content and available functionality. On this background the Forest Data Bank (BDL) in Poland has been described: its main objectives, information content and the technology which is used to share data. We have analyzed the current state of gathering and sharing of information on forests in the world and factors influencing their development. Particular attention has been paid to the BDL, which as compared with other databases at the national level, is one of the richer and more complete sources of information about forests

Some practical solutions practised and proposed by BULiGL for protection of nature in forests

Przedmiotem niniejszej pracy są zagadnienia dotyczące w szczególności sporządzania prognozy oddziaływania na środowisko, w tym także stopień szczegółowości informacji tam zawartych, a także niektórych kryteriów weryfikacji proponowanych rozwiązań.This work presents the issues, in particular the preparation of environmental impact forecasts, including the degree of detail contained therein, as well as some criteria for the verification of the proposed solutions