O nascimento prematuro contribui significativamente para o aumento de morbidades associadas ao desenvolvimento motor, tornando fundamental o acompanhamento contínuo destas crianças. Desta forma, a avaliação baropodométrica, por consistir em um método quantitativo de controle postural pode trazer vantagens para o diagnóstico e acompanhamento do desenvolvimento motor de crianças. Este estudo teve por objetivo desenvolver um protocolo de avaliação motora através dos dados e índices baropodométricos em crianças nascidas pré-termo. Foi realizado um estudo descritivo, onde foram avaliadas 103 crianças entre 24 e 59 meses. Destas, 40 nascidas pré-termo e 63 crianças nascidas a termo. Durante a seleção da amostra, foi preenchida uma ficha de avaliação correspondente ao pré-termo grupo e um questionário com relatos dos pais no grupo a termo. Após, foram aferidos massa corporal e estatura, seguida da aplicação da Escala de Desenvolvimento Motor. Por fim, a baropodometria foi realizada na forma estática, em três repetições, os quais consistiram de 5 segundos de adaptação da criança dobre a placa e 30 segundos onde foram aferidos dados de análise estática: pressão plantar e área do centro de oscilação corporal. Após, as pressões plantares foram transformadas em índices, o índice ânteroposterior foi definido pelas pressões plantares anterior e posterior: IAP= 1-2*│0,6-P│; e o índice látero-lateral, por sua vez, foi definido pelas pressões plantares laterais direita e esquerda: ILL= 1-│LD-LE│. Após a avaliação os dados foram submetidos ao teste de normalidade das distribuições de Shapiro-Wilk, após verificada a distribuição não-normal, foi aplicado o teste de Mann-Whitney para verificar diferença entre os grupos, a associação entre os valores obtidos pelo baropodômetro, Escala do Desenvolvimento Motor, e as principais características e intercorrências do grupo pré-termo foi verificada através da correlação de Spearman. Foi observada diferença significativa nos valores de ILL (p=0,000) entre crianças nascidas a termo e crianças nascidas pré-termo, e que esta diferença possui correlação moderada com a idade gestacional (ρ=0,304), em relação ao centro de oscilação de pressão, crianças nascidas a termo apresentaram menor oscilação quando comparado a idade cronológica (ρ=-0,354), sendo que esta relação foi contrária em crianças nascidas pré-termo (ρ=0,336). Quando analisado somente o grupo pré-termo, foi verificado que o ILL apresentou correlação moderada e inversa com o tempo de internação (ρ=-0,353) e com o tempo de ventilação mecânica (ρ=-0,317) e a aérea do centro de oscilação de pressão apresentou correlação moderada e direta com o tempo de ventilação não invasiva (ρ=0,341). A massa ao nascer apresentou correlação moderada com o ILL (ρ=0,359) e também com a idade motora (ρ=0,323) e o quociente motor (ρ=0,341) e correlação forte com a IG (ρ=0,898) em contrapartida o peso atual apresentou correlação moderada com o quociente motor (ρ=0,310), e a IG (ρ=0,381) e correlação forte com a idade motora (ρ=0,555) e a idade cronológica (ρ=0,613). Houve diferença significativa em relação a idade de aquisição da marcha das crianças que precisaram de acompanhamento fisioterapêutico das que não precisaram (p=0,013). Um índice ILL menor em prematuros, pode estar relacionado ao tempo de internação e ventilação mecânica, além da massa ao nascer, já a maior aérea do centro de oscilação de pressão possui correlação com o tempo de ventilação não invasiva. Também pode-se perceber que a massa atual e a idade cronológica influenciaram mais no desenvolvimento motor que a massa ao nascer e a idade gestacional em crianças prematuras. / Preterm birth contributes significantly to the increase of morbidities associated with motor development, making essential the continuous monitoring of these children. Thus, baropodometry analysis by consisting of a quantitative method for postural control can be advantageous for the diagnosis and monitoring of engine development of children. This study aimed to develop a motor evaluation protocol through the data and baropodometric indexes in preterm infants. It was a descriptive study, which were evaluated 103 children between 24 and 59 months. Of these, 40 preterm and 63 term infants. During the sample selection was completed an evaluation form with data from medical records corresponding to the pre-term group and a questionnaire to parents on group term. After, body mass and height were measured, then the implementation of the Motor Development Scale. Finally, baropodometry was held in static form, with three replicates, which consisted of 5 seconds of child adjustment bend the plate and 30 seconds which were measured static analysis data: plantar pressure and pressure swing center area. After, the plantar pressures were transformed into indexes, the anteroposterior index was defined by the anterior and posterior plantar pressures: API = 1-2 * │0,6-P│; and side side index, in turn, defined by the right and left side planter pressure: SSI = 1- │RS-LS│. After evaluating, the data were submitted to normality test of Shapiro-Wilk distributions, being checked the non-normal distribution, the Mann-Whitney test was used to verify differences between groups, the association between the values obtained by baropodometry analysis, Motor Development Scale, and the main characteristics and complications of preterm group was verified by Spearman correlation. Significant difference in the values of SSI (p = 0.000) among term infants and infants born preterm were observed, and this difference has moderate correlation with gestational age (ρ = 0.304) compared to the pressure oscillation center , full-term babies showed less fluctuation compared to chronological age (ρ = -0.354), and this relationship was contrary in preterm children (ρ = 0.336).When only analyzed the preterm group, it was found that the SSI had moderate and inverse correlation with the length of stay (ρ = -0.353) and the duration of mechanical ventilation (ρ = -0.317) and the air oscillation center pressure showed moderate and direct correlation with noninvasive ventilation time (ρ = 0.341).The mass at birth showed moderate correlation with SSI (ρ = 0.359) and also with the motor age (ρ = 0.323) and the ratio engine (ρ = 0.341) and strong correlation with gestational age (ρ = 0.898) in contrast current weight showed moderate correlation with the motor quotient (ρ = 0.310) and gestational age(ρ = 0.381) and strong correlation with the motor age (ρ = 0.555) and chronological age (ρ = 0.613). There was significant difference in the age of acquisition of march of the children who needed physical therapy monitoring of those who did not needed (p = 0.013). A smaller SSI index in premature infants, may be related to hospitalization time and mechanical ventilation, in addition to mass at birth, already the largest air pressure oscillation center has correlation with noninvasive ventilation time.It may also be seen that the current mass and chronological age influenced more motor development than the mass at birth and gestational age in preterm children.

An automated manufacturing industry makes use of many interacting moving parts and sensors. Data from these sensors generate complex multidimensional data in the production environment. This data is difficult to interpret and also difficult to find patterns in. This project provides tools to get a deeper understanding of Swedsafe’s production data, a company involved in an automated manufacturing business. The project is based on and will show the potential of the multidimensional production data. The project mainly consists of predicting deviations from predefined threshold values in Swedsafe’s production data. Machine learning is a good method of finding relationships in complex datasets. Supervised machine learning classification is used to predict deviation from threshold values in the data. An investigation is conducted to identify the classifier that performs best on Swedsafe's production data. The technique sliding window is used for managing time series data, which is used in this project. Apart from predicting deviations, this project also includes an implementation of live graphs to easily get an overview of the production data. A steady production with stable process values is important. So being able to monitor and predict events in the production environment can provide the same benefit for other manufacturing companies and is therefore suitable not only for Swedsafe. The best performing machine learning classifier tested in this project was the Random Forest classifier. The Multilayer Perceptron did not perform well on Swedsafe’s data, but further investigation in recurrent neural networks using LSTM neurons would be recommended. During the projekt a web based application displaying the sensor data in live graphs is also developed.

MPH / Department of Public Health / Autism spectrum disorder (ASD) is a life-long neurodevelopmental disorder, which does not affect the child only but the caregiver more. ASD characterized by impairments in social interactions, communication and repetitive behaviour. Therefore, caring for a child diagnosed with ASD can be a very challenging experience for caregiver especially when knowledge about the condition is limited. The aim of the study was to explore experiences of caregivers for children diagnosed with ASD in the Ehlanzeni District, Mpumalanga Province. The study adopted a qualitative approach, wherein data was collected using face-to-face semi-structured interviews, in which an interview guide was used. Participants were selected purposively from the three different schools and data was analysed using thematic content analysis. Twelve (12) participants were interviewed for the study. The caregivers’ children were aged 5-12 years. Ethical considerations and measures to ensure trustworthiness were adhered to throughout the study. The study findings indicated that caregivers for children diagnosed with ASD experienced psychological stress, social isolation and stigma, financial burden, lack of family support, services for children with ASD were perceived not to be accessible and available. The findings also indicated that there is limited knowledge of ASD amongst caregivers, health professionals and the community at large. Therefore, more awareness campaigns need to be done on ASD to increase knowledge on the condition. Furthermore, the study recommends that support groups for caregivers of children diagnosed with ASD should be formed and that information regarding a range of inexpensive interventions and educational programs should be made available for caregivers and their children, as well as continuous dissemination of information amongst caregivers. However, limited statistical information on ASD is available on the South African context. / NRF

Der Beitrag unterteilt sich in zwei Teile: Teil 1 (vgl. Informationen/07; 1976,05) und Teil 2 (cp. Informationen/07; 1976,06). Teil 1 enthält eine Einleitung und Grenzwertsätze für unabhängige und identisch verteilte Zufallsgrößen und die Übertragung der betrachteten Grenzwertsätze auf den Fall der Existenz einseitiger Momente. Teil 2 enthält Grenzwertsätze für mittlere Abweichungen für Summen unabhängiger nichtidentisch verteilter Zufallsgrößen (Serienschema) und eine Diskussion der erhaltenen Ergebnisse und schließlich einige Literaturangaben. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und identisch verteilte Zufallsgrößen mit Erwartungswert 0 und Streuung 1 und endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_i derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsätzen in verschiedenen Fällen angeben können, wobei sich der Index i in L_i auf folgende fünf Fälle bezieht: kleine x, mittlere Abweichungen für x, große Abweichungen für x, kleine n und große n. Im Fall der Existenz einseitiger Momente werden obere Schanken für 1-F_n(x) angegeben für x>D_m*n^(1/2)*ln(n) bzw. x>D_m*n^(1/2)*(ln(n))^(1/2), womit Ergebnisse von S.V.NAGAEV(1965) präzisiert werden. Der Beitrag unterteilt sich in zwei Teile: Teil 1 (vgl. Informationen/07; 1976,05) und Teil 2 (cp. Informationen/07; 1976,06). Teil 1 enthält eine Einleitung und Grenzwertsätze für unabhängige und identisch verteilte Zufallsgrößen und die Übertragung der betrachteten Grenzwertsätze auf den Fall der Existenz einseitiger Momente. Teil 2 enthält Grenzwertsätze für mittlere Abweichungen für Summen unabhängiger nichtidentisch verteilter Zufallsgrößen (Serienschema) und eine Diskussion der erhaltenen Ergebnisse und schließlich einige Literaturangaben. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und identisch verteilte Zufallsgrößen mit Erwartungswert 0 und Streuung 1 und endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_i derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsätzen in verschiedenen Fällen angeben können, wobei sich der Index i in L_i auf folgende fünf Fälle bezieht: kleine x, mittlere Abweichungen für x, große Abweichungen für x, kleine n und große n. Im Fall der Existenz einseitiger Momente werden obere Schanken für 1-F_n(x) angegeben für x>D_m*n^(1/2)*ln(n) bzw. x>D_m*n^(1/2)*(ln(n))^(1/2), womit Ergebnisse von S.V.NAGAEV(1965) präzisiert werden.:6. Grenzwertsätze für mittlere Abweichungen für verschieden verteilte Zufallsgrößen S. 1 7. Beweise zum Abschnitt 6 S. 2 8. Diskussion der Ergebnisse S. 6 Literatur S. 10 / The paper is divided in two parts: part 1 (cp. Informationen/07; 1976,05) and part 2 (cp. Informationen/07; 1976,06). Part 1 contains an introduction and limit theorems for iid random variables and the transfer of the considered limit theorems to the case of the existence of onesided moments. Part 2 contains limit theorems of moderate deviations for sums of series of non iid random variables and a discussion of all obtained results in part 1 and 2 and finally some references. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are iid random variables with mean 0 and variance 1 and with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_i are computed such that we have an error estimate in the nonuniform central limit theorem with the L_i, where i corresponds to the five cases considered: small x, moderate deviations for x, large deviations for x, small n , large n. Additional upper bounds for 1-F_n(x) are obtained if the one-sided moments of order m, m>2, are finite and if x>D_m*n^(1/2)*ln(n) and x>D_m*n^(1/2)*(ln(n))^(1/2) respectively improving results by S.V.NAGAEV (1965).:6. Grenzwertsätze für mittlere Abweichungen für verschieden verteilte Zufallsgrößen S. 1 7. Beweise zum Abschnitt 6 S. 2 8. Diskussion der Ergebnisse S. 6 Literatur S. 10

Der Beitrag unterteilt sich in zwei Teile: Teil 1 (vgl. Informationen/07; 1976,05) und Teil 2 (cp. Informationen/07; 1976,06). Teil 1 enthält eine Einleitung und Grenzwertsätze für unabhängige und identisch verteilte Zufallsgrößen und die Übertragung der betrachteten Grenzwertsätze auf den Fall der Existenz einseitiger Momente. Teil 2 enthält Grenzwertsätze für mittlere Abweichungen für Summen unabhängiger nichtidentisch verteilter Zufallsgrößen (Serienschema) und eine Diskussion der erhaltenen Ergebnisse und schließlich einige Literaturangaben. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und identisch verteilte Zufallsgrößen mit Erwartungswert 0 und Streuung 1 und endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_i derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsätzen in verschiedenen Fällen angeben können, wobei sich der Index i in L_i auf folgende fünf Fälle bezieht: kleine x, mittlere Abweichungen für x, große Abweichungen für x, kleine n und große n. Im Fall der Existenz einseitiger Momente werden obere Schanken für 1-F_n(x) angegeben für x>D_m*n^(1/2)*ln(n) bzw. x>D_m*n^(1/2)*(ln(n))^(1/2), womit Ergebnisse von S.V.NAGAEV(1965) präzisiert werden.:1. Einführung S. 2 2. Grenzwertsätze für identisch verteilte Zufallsgrößen S. 3 3. Übertragung der formulierten Grenzwertsätze auf den Fall der Existenz einseitiger Momente S. 6 4. Beweis zum Abschnitt 2 S. 8 5. Beweise zum Abschnitt 3 S. 13 / The paper is divided in two parts: part 1 (cp. Informationen/07; 1976,05) and part 2 (cp. Informationen/07; 1976,06). Part 1 contains an introduction and limit theorems for iid random variables and the transfer of the considered limit theorems to the case of the existence of onesided moments. Part 2 contains limit theorems of moderate deviations for sums of series of non iid random variables and a discussion of all obtained results in part 1 and 2 and finally some references. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are iid random variables with mean 0 and variance 1 and with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_i are computed such that we have an error estimate in the nonuniform central limit theorem with the L_i, where i corresponds to the five cases considered: small x, moderate deviations for x, large deviations for x, small n , large n. Additional upper bounds for 1-F_n(x) are obtained if the one-sided moments of order m, m>2, are finite and if x>D_m*n^(1/2)*ln(n) and x>D_m*n^(1/2)*(ln(n))^(1/2) respectively improving results by S.V.NAGAEV (1965).:1. Einführung S. 2 2. Grenzwertsätze für identisch verteilte Zufallsgrößen S. 3 3. Übertragung der formulierten Grenzwertsätze auf den Fall der Existenz einseitiger Momente S. 6 4. Beweis zum Abschnitt 2 S. 8 5. Beweise zum Abschnitt 3 S. 13

Cette thèse s'inscrit dans le domaine des probabilités et des statistiques, et plus précisément des matrices aléatoires. Dans la première partie, on étudie les grandes déviations de la mesure spectrale de matrices de covariance $XX^*$, où $X$ est une matrice aléatoire rectangulaire à coefficients i.i.d. ayant une queue de probabilité en $exp(-at^{alpha})$, $alpha in ]0,2[$. On établit un principe de grandes déviations analogue à celui de Bordenave et Caputo, de vitesse $n^{1+alpha/2}$ et de fonction de taux explicite faisant intervenir la convolution libre rectangulaire. La démonstration repose sur un résultat de quantification de la liberté asymptotique dans le modèle information-plus-bruit. La seconde partie de cette thèse est consacrée à l'étude du comportement en temps long de la solution de l'équation de Fokker-Planck libre en présence du potentiel quartique $V(x) = frac14 x^4 + frac{c}{2} x^2$ avec $c ge -2$. On montre que quand $t to +infty$, la solution $mu_t$ de cette équation aux dérivées partielles converge en distance de Wasserstein vers la mesure d'équilibre associée au potentiel $V$. Ce résultat fournit un premier exemple de convergence en temps long de la solution de l'équation des milieux granulaires en présence d'un potentiel non convexe et d'une interaction logarithmique. Sa démonstration utilise notamment des techniques de probabilités libres. / This thesis lies within the field of probability and statistics, and more precisely of random matrix theory. In the first part, we study the large deviations of the spectral measure of covariance matrices XX*, where X is a rectangular random matrix with i.i.d. coefficients having a probability tail like $exp(-at^{alpha})$, $alpha in (0,2)$. We establish a large deviation principle similar to Bordenave and Caputo's one, with speed $n^{1+alpha/2}$ and explicit rate function involving rectangular free convolution. The proof relies on a quantification result of asymptotic freeness in the information-plus-noise model. The second part of this thesis is devoted to the study of the long-time behaviour of the solution to free Fokker-Planck equation in the setting of the quartic potential $V(x) = frac14 x^4 + frac{c}{2} x^2$ with $c ge -2$. We prove that when $t to +infty$, the solution $mu_t$ to this partial differential equation converge in Wasserstein distance towards the equilibrium measure associated to the potential $V$. This result provides a first example of long-time convergence for the solution of granular media equation with a non-convex potential and a logarithmic interaction. Its proof involves in particular free probability techniques.

Eine stetig gleichbleibende hohe Qualität zu fertigen, ist erklärtes Ziel des Spritzgießgewer-bes. Aus technischen oder wirtschaftlichen Gründen ist es jedoch nicht möglich, für konstan-te Produktionsrahmenbedingungen zu sorgen. Die effizienteste Methode ist , die Schwan-kungen über die Wahl der richtigen Prozessführungsmethode auszugleichen. Im ersten Teil der Arbeit konnte herausgefunden werden, welche praxisrelevanten Störgrö-ßen einen Einfluss auf den Spritzgießprozess haben und wie sie sich auswirken. Bei den Materialparametern sind Änderungen der Viskosität (15 %) und der Einfriertemperatur des Materials (4 °C) am Einzug festzustellen. Zusätzlich veränderte sich das Messverhalten der Drucksensoren, wodurch ein Drift von 5 bar entstand. Störgrößenbedingt änderten sich auch die Prozesstemperaturen um 1 °C. Im zweiten Teil der Arbeit werden diverse, während der Arbeit entwickelte, Prozessfüh-rungsmethoden miteinander verglichen. Aufgabe war es, die im ersten Teil gefundenen rea-len störgrößenbedingten Einflüsse zu kompensieren. Es stellte sich heraus, dass sich ledig-lich die materialbedingten Schwankungen nicht ausgleichen lassen. Zumindest können de-ren Auswirkungen durch eine Regelung der werkstoffnahen Parameter abschwächt werden. / To produce a steady consistent high quality is the declared goal of the injection moulding industry. For technical or economic reasons, it is not possible to ensure constant production framework conditions. The proper method is to compensate the variable influences with the choice of the correct process control method. The first part of the thesis focuses on the analysis of the different disturbances factors. The investigation showed that the material property, melt viscosity, varies about 15% and the recrystallisation temperature arises a deviation of 4°C. Another changes could be measured in the offset of the pressure sensor (5 bar) and the process temperatures (1°C). The next goal was to find a suitable control method to balance these intermittencies. The test series showed clearly that changes in the material properties could not be compensated. But there impact toward the quality could be extenuated with a constant course of the process parameter in the cavity.

No description available.

Cette thèse est dévolue à l'étude de certaines propriétés asymptotiques du processus autorégressif d'ordre p. Ce dernier qualifie communément une suite aléatoire $(Y_{n})$ définie sur $\dN$ ou $\dZ$ et entièrement décrite par une combinaison linéaire de ses $p$ valeurs passées, perturbée par un bruit blanc $(\veps_{n})$. Tout au long de ce mémoire, nous traitons deux problématiques majeures de l'étude de tels processus : l'\textit{autocorrélation résiduelle} et la \textit{stationnarité}. Nous proposons en guise d'introduction un survol nécessaire des propriétés usuelles du processus autorégressif. Les deux chapitres suivants sont consacrés aux conséquences inférentielles induites par la présence d'une autorégression significative dans la perturbation $(\veps_{n})$ pour $p=1$ tout d'abord, puis pour une valeur quelconque de $p$, dans un cadre de stabilité. Ces résultats nous permettent d'apposer un regard nouveau et plus rigoureux sur certaines procédures statistiques bien connues sous la dénomination de \textit{test de Durbin-Watson} et de \textit{H-test}. Dans ce contexte de bruit autocorrélé, nous complétons cette étude par un ensemble de principes de déviations modérées liées à nos estimateurs. Nous abordons ensuite un équivalent en temps continu du processus autorégressif. Ce dernier est décrit par une équation différentielle stochastique et sa solution est plus connue sous le nom de \textit{processus d'Ornstein-Uhlenbeck}. Lorsque le processus d'Ornstein-Uhlenbeck est lui-même engendré par une diffusion similaire, cela nous permet de traiter la problématique de l'autocorrélation résiduelle dans le processus à temps continu. Nous inférons dès lors quelques propriétés statistiques de tels modèles, gardant pour objectif le parallèle avec le cas discret étudié dans les chapitres précédents. Enfin, le dernier chapitre est entièrement dévolu à la problématique de la stationnarité. Nous nous plaçons dans le cadre très général où le processus autorégressif possède une tendance polynomiale d'ordre $r$ tout en étant engendré par une marche aléatoire intégrée d'ordre $d$. Les résultats de convergence que nous obtenons dans un contexte d'instabilité généralisent le \textit{test de Leybourne et McCabe} et certains aspects du \textit{test KPSS}. De nombreux graphes obtenus en simulations viennent conforter les résultats que nous établissons tout au long de notre étude. / This thesis is devoted to the study of some asymptotic properties of the $p-$th order \textit{autoregressive process}. The latter usually designates a random sequence $(Y_{n})$ defined on $\dN$ or $\dZ$ and completely described by a linear combination of its $p$ last values and a white noise $(\veps_{n})$. All through this manuscript, one is concerned with two main issues related to the study of such processes: \textit{serial correlation} and \textit{stationarity}. We intend, by way of introduction, to give a necessary overview of the usual properties of the autoregressive process. The two following chapters are dedicated to inferential consequences coming from the presence of a significative autoregression in the disturbance $(\veps_{n})$ for $p=1$ on the one hand, and then for any $p$, in the stable framework. These results enable us to give a new light on some statistical procedures such as the \textit{Durbin-Watson test} and the \textit{H-test}. In this autocorrelated noise framework, we complete the study by a set of moderate deviation principles on our estimates. Then, we tackle a continuous-time equivalent of the autoregressive process. The latter is described by a stochastic differential equation and its solution is the well-known \textit{Ornstein-Uhlenbeck process}. In the case where the Ornstein-Uhlenbeck process is itself driven by an Ornstein-Uhlenbeck process, one deals with the serial correlation issue for the continuous-time process. Hence, we infer some statistical properties of such models, keeping the parallel with the discrete-time framework studied in the previous chapters as an objective. Finally, the last chapter is entirely devoted to the stationarity issue. We consider the general autoregressive process with a polynomial trend of order $r$ driven by a random walk of order $d$. The convergence results in the unstable framework generalize the \textit{Leybourne and McCabe test} and some angles of the \textit{KPSS test}. Many graphs obtained by simulations come to strengthen the results established all along the study.

In the light of the child's self-esteem that is affected by traumatic events, the goal of the research was to explore and describe the self-esteem of children orphaned by HIV/AIDS. The researcher made use of a quantitative research method. 30 (N=30) respondents, both male (n=16) and female (n=14), between the ages of 11 to 15, were randomly sampled for inclusion in the study. Each participant completed a self-report measure of self-esteem, The Culture-free Self-esteem Inventory for Children, which yielded a score of Global Self-esteem, as well as in four sub-domains including: General, Social, Academic and Parent-related Self-esteem. The results of this study demonstrated that the participants experienced a lowered self-esteem. These findings were explored in light of a literature review, after which conclusions and recommendations were provided. / Social Work / M. Diac. (Play Therapy)