This thesis is concerned with boundary crossing probabilities and first crossing time densities for stochastic processes. This is a classical problem in probability that goes back to the famous ballot problem (first studied by W. A. Whitworth (1878) and J. Bertrand (1887)) and has numerous applications in diverse areas including mathematical statistics and financial mathematics. Our main objective is the study of approximation methods and control of the resulting approximation error for boundary crossing probabilities where a closed-form solution is unavailable. This leads to the study of bounds for the density of the first crossing time of the boundary, which in turn leads to the derivation of some analytic properties of the densities. This thesis presents a whole suite of closely related new results obtained when working on the outlined research program. (For complete abstract open document).

Neste trabalho são investigados alguns aspectos relacionados com a programação de tempos de semáforos isolados. A seguir são comentados os principais resultados obtidos. Os valores obtidos na cidade de São Carlos são os seguintes: tempo médio total (no início e no final) perdido no verde mais amarelo por fase veicular nos semáforos igual a 3,12 s (interseção em nível e fluxo sem conversão); velocidade média dos pedestres na travessia em semáforos igual a 1,28 m/s e velocidade correspondente ao 85 percentil igual a 1,00 m/s. Com exceção de alguns casos especiais, os valores do atraso fornecidos pelos métodos: Webster, HCM-2000, Simulador Integration e Simulador Corsim são da mesma magnitude e, portanto, perfeitamente viáveis de serem utilizados nos estudos práticos. Na determinação dos tempos que compõem a fase destinada à travessia de pedestres em semáforos, os métodos Ferraz e MUTCD são mais indicados que os métodos Webster/Denatran e CET-SP, uma vez que proporcionam adequada segurança sem \"assustar\" os pedestres e com o mínimo de prejuízo à capacidade do fluxo veicular. O emprego de fase exclusiva para pedestres em semáforos com duas fases veiculares leva aos seguintes acréscimos aproximados nos valores do atraso médio dos veículos: 40% para fluxos veiculares até 1000 v/h, 25% para fluxos veiculares da ordem de 1100 v/h e 20% para fluxos veiculares da ordem de 1200 v/h. / In this research some aspects related to time programming of single traffic lights are investigated. The main results are commented as follows. The values obtained in the city of São Carlos are: total average lost time (in the beginning and in the end) in the green and yellow phases in each vehicular signal phase equal to 3.12 s (level intersection and flow without conversion), pedestrians average speed on the traffic lights crossing equal to 1.28 m/s and speed corresponding to the 85º percentile equal to 1.00 m/s. Except for some special cases, the values of the delay provided by the Webster, HCM-2000, Simulator Integration and Simulator Corsim methods are of the same magnitude and, therefore, they are perfectly feasible to use in practical studies. In determining the periods of the pedestrian crossing stage for the traffic signals, the Ferraz and MUTCD methods are more indicated than the Webster/Denatran and CET-SP methods, since they provide appropriate safety without \"scaring\" the pedestrians and with minimal damage to the vehicular flow capacity. The use of exclusive pedestrian phase at two vehicular stage signals leads to the following approximate increases in the values of the vehicles average delay: 40% to vehicle flow up to 1000 v/h, 25% for vehicle flow about 1100 v/h, and 20% for vehicle flow about 1200 v/h. In this research some aspects related to time programming of single traffic lights are investigated.

Neste trabalho são investigados alguns aspectos relacionados com a programação de tempos de semáforos isolados. A seguir são comentados os principais resultados obtidos. Os valores obtidos na cidade de São Carlos são os seguintes: tempo médio total (no início e no final) perdido no verde mais amarelo por fase veicular nos semáforos igual a 3,12 s (interseção em nível e fluxo sem conversão); velocidade média dos pedestres na travessia em semáforos igual a 1,28 m/s e velocidade correspondente ao 85 percentil igual a 1,00 m/s. Com exceção de alguns casos especiais, os valores do atraso fornecidos pelos métodos: Webster, HCM-2000, Simulador Integration e Simulador Corsim são da mesma magnitude e, portanto, perfeitamente viáveis de serem utilizados nos estudos práticos. Na determinação dos tempos que compõem a fase destinada à travessia de pedestres em semáforos, os métodos Ferraz e MUTCD são mais indicados que os métodos Webster/Denatran e CET-SP, uma vez que proporcionam adequada segurança sem \"assustar\" os pedestres e com o mínimo de prejuízo à capacidade do fluxo veicular. O emprego de fase exclusiva para pedestres em semáforos com duas fases veiculares leva aos seguintes acréscimos aproximados nos valores do atraso médio dos veículos: 40% para fluxos veiculares até 1000 v/h, 25% para fluxos veiculares da ordem de 1100 v/h e 20% para fluxos veiculares da ordem de 1200 v/h. / In this research some aspects related to time programming of single traffic lights are investigated. The main results are commented as follows. The values obtained in the city of São Carlos are: total average lost time (in the beginning and in the end) in the green and yellow phases in each vehicular signal phase equal to 3.12 s (level intersection and flow without conversion), pedestrians average speed on the traffic lights crossing equal to 1.28 m/s and speed corresponding to the 85º percentile equal to 1.00 m/s. Except for some special cases, the values of the delay provided by the Webster, HCM-2000, Simulator Integration and Simulator Corsim methods are of the same magnitude and, therefore, they are perfectly feasible to use in practical studies. In determining the periods of the pedestrian crossing stage for the traffic signals, the Ferraz and MUTCD methods are more indicated than the Webster/Denatran and CET-SP methods, since they provide appropriate safety without \"scaring\" the pedestrians and with minimal damage to the vehicular flow capacity. The use of exclusive pedestrian phase at two vehicular stage signals leads to the following approximate increases in the values of the vehicles average delay: 40% to vehicle flow up to 1000 v/h, 25% for vehicle flow about 1100 v/h, and 20% for vehicle flow about 1200 v/h. In this research some aspects related to time programming of single traffic lights are investigated.

Dans un contexte de vieillissement démographique et de mutation des modes de déplacements urbains majorant la place du piéton, ce travail de thèse vise à mieux comprendre les caractéristiques comportementales et biomécaniques de la traversée de rue des piétons âgés. La méthodologie est essentiellement expérimentale. Si quelques données ont été recueillies en laboratoire ou en environnement naturel, l'étude principale a été conduite dans un simulateur immersif de réalité projetée, outil dénommé Simulateur de Rues pour Piétons (SRP). La hauteur de trottoir est modulable. Le dispositif intègre différents outils de mesures, tels des plates-formes de force et un système d'analyse gestuelle en trois dimensions. Hors simulateur, la comparaison des temps de traversée réelle et estimée, sur un champ de marche, révèle l'occurrence d'un risque de sous-estimation a priori du temps nécessaire chez certains seniors. L'expérience en simulateur confirme l'importance de la modulation exercée par le vieillissement sur la perception du temps en tant que déterminant des estimations a posteriori des temps de traversées quantifiées via la sensation de mise en danger. En simulateur, les seniors adoptent un comportement sécuritaire, requérant des intervalles temporels plus longs pour décider d'initier une traversée. Dans des conditions de trafic favorables, ils marchent plus rapidement que les jeunes. Leurs marges de sécurité sont plus grandes. L'approche biomécanique, révèle des différences intergroupes, dont certaines sont potentiellement à risque (ex. la flexion plantaire) alors que d’autres (ex. les rotations exploratoires) participent à l’adaptation. / In the framework of population ageing and increased importance attached to walking in urban cities, the aim of this PhD work is to better understand behavioral and biomechanical characteristics of older pedestrian road crossing. We mostly used the experimental method. Some data were collected in laboratory or natural environment, but the main study was performed in an immersive road crossing simulator with projected reality: the Simulator of Road for Pedestrians (SRP). The curb height was adjustable. The device integrated various biomechanical measurement tools such as force plates and 3D-gait analysis systems. The real and the imagined crossing times were compared in a task performed outside the simulator. It reveals that some seniors underestimated their crossing time. The experiment within the simulator confirmed the relevance of the age-related modulation of the crossing time perception, which was indirectly estimated by the feeling of endangerment. Inside the simulator, the road crossing behavior of the elderly participants was safe, requiring longer temporal intervals for deciding to initiate the crossing. In favorable traffic gap conditions, they walked more quickly than the younger participants and their safety margins were larger. The biomechanical approach revealed intergroup differences, some of which inducing potential risks (e.g., plantar flexion) while others (e.g., exploratory rotations) participated in the coping.

Negative cloud-to-ground (CG) lightning flashes transport negative charge from cloud to ground. Negative ground flashes typically involve various processes identified as preliminary breakdown, stepped leader, return stroke, dart leader, dart-stepped leader, subsequent return stroke, and cloud activity between strokes, such as regular pulse trains and chaotic pulse trains. These processes can be identified through their electromagnetic field signatures. The main focus of this thesis is to document the features and understand the origin of electromagnetic fields, especially the chaotic pulse trains, generated by lightning flashes. Electric field measurements have been used to study lightning flashes in Sweden. The equipment was a parallel flat plate antenna with an analog filter buffer circuit, connected to a digital high speed oscilloscope. Four simultaneous measurements were made: wideband measurement of the E-field (the vertical component) and its time derivative dE/dt, and two narrowband measurements of the E-field, centred around 3 MHz and 30 MHz. Fourier and wavelet transforms were used in the analysis of the measured data. The results show that preliminary breakdown pulses are stronger radiators at 3 MHz and 30 MHz than are the return strokes. A comparison of our results with those of previous studies obtained in different geographical regions clearly shows that the strength of preliminary breakdown pulses decreases with decreasing latitude. It is higher in the temperate regions (Sweden, for instance) and lower in the tropical regions. A comparison of the time derivatives of preliminary breakdown pulses and of the narrow bipolar pulses shows that the physical origin of these two types of pulse is different, even though they may have similar appearances in the broadband fields. This thesis introduces a new procedure to estimate the zero-crossing time of the lightning-generated radiation fields. The procedure is based on the fact that the time integral of the radiation fields generated by a discharge event whose duration is finite is equal to zero, and the zero-crossing time corresponds to the time when the peak of the integral is reached. In addition to tabulating the various statistical parameters and features of Chaotic Pulse Trains (CPTs), it is shown that these pulse trains are created by the simultaneous propagation of several dart-stepped leader type discharges in the cloud. Each dart-stepped leader type discharge generates a Regular Pulse Train (RPT), and these pulse trains combine randomly in time to generate CPTs. This conclusion is based on the results obtained by numerical simulations and by analysing the signatures of these pulse trains using Fourier and wavelet transformations. The results presented in this thesis show that electromagnetic fields, even those measured from a single station, can be used to extract information concerning the physical processes that gave rise to these fields.

Dans cette thèse, nous proposons des modèles probabilistes et statistiques d’analyse de données multidimensionnelles pour la prévision de l’incertitude sur les trajectoires d’aéronefs. En supposant que pendant le vol, chaque aéronef suit sa trajectoire 3D contenue dans son plan de vol déposé, nous avons utilisé l’ensemble des caractéristiques de l’environnement des vols comme variables indépendantes pour expliquer l’heure de passage des aéronefs sur les points de leur trajectoire de vol prévue. Ces caractéristiques sont : les conditions météorologiques et atmosphériques, les paramètres courants des vols, les informations contenues dans les plans de vol déposés et la complexité de trafic. Typiquement, la variable dépendante dans cette étude est la différence entre les instants observés pendant le vol et les instants prévus dans les plans de vol pour le passage des aéronefs sur les points de leur trajectoire prévue : c’est la variable écart temporel. En utilisant une technique basée sur le partitionnement récursif d’un échantillon des données, nous avons construit quatre modèles. Le premier modèle que nous avons appelé CART classique est basé sur le principe de la méthode CART de Breiman. Ici, nous utilisons un arbre de régression pour construire une typologie des points des trajectoires des vols en fonction des caractéristiques précédentes et de prévoir les instants de passage des aéronefs sur ces points. Le second modèle appelé CART modifié est une version améliorée du modèle précédent. Ce dernier est construit en remplaçant les prévisions calculées par l’estimation de la moyenne de la variable dépendante dans les nœuds terminaux du modèle CART classique par des nouvelles prévisions données par des régressions multiples à l’intérieur de ces nœuds. Ce nouveau modèle développé en utilisant l’algorithme de sélection et d’élimination des variables explicatives (Stepwise) est parcimonieux. En effet, pour chaque nœud terminal, il permet d’expliquer le temps de vol par des variables indépendantes les plus pertinentes pour ce nœud. Le troisième modèle est fondé sur la méthode MARS, modèle de régression multiple par les splines adaptatives. Outre la continuité de l’estimateur de la variable dépendante, ce modèle permet d’évaluer les effets directs des prédicteurs et de ceux de leurs interactions sur le temps de passage des aéronefs sur les points de leur trajectoire de vol prévue. Le quatrième modèle utilise la méthode d’échantillonnage bootstrap. Il s’agit notamment des forêts aléatoires où pour chaque échantillon bootstrap de l’échantillon de données initial, un modèle d’arbre de régression est construit, et la prévision du modèle général est obtenue par une agrégation des prévisions sur l’ensemble de ces arbres. Malgré le surapprentissage observé sur ce modèle, il est robuste et constitue une solution au problème d’instabilité des arbres de régression propre à la méthode CART. Les modèles ainsi construits ont été évalués et validés en utilisant les données test. Leur application au calcul des prévisions de la charge secteur en nombre d’avions entrants a montré qu’un horizon de prévision d’environ 20 minutes pour une fenêtre de temps supérieure à 20 minutes permettait d’obtenir les prévisions avec des erreurs relatives inférieures à 10%. Parmi ces modèles, CART classique et les forêts aléatoires présentaient de meilleures performances. Ainsi, pour l’autorité régulatrice des courants de trafic aérien, ces modèles constituent un outil d’aide pour la régulation et la planification de la charge des secteurs de l’espace aérien contrôlé. / In this thesis we propose probabilistic and statistic models based on multidimensional data for forecasting uncertainty on aircraft trajectories. Assuming that during the flight, aircraft follows his 3D trajectory contained into his initial flight plan, we used all characteristics of flight environment as predictors to explain the crossing time of aircraft at given points on their planned trajectory. These characteristics are: weather and atmospheric conditions, flight current parameters, information contained into the flight plans and the air traffic complexity. Typically, in this study, the dependent variable is difference between actual time observed during flight and planned time to cross trajectory planned points: this variable is called temporal difference. We built four models using method based on partitioning recursive of the sample. The first called classical CART is based on Breiman CART method. Here, we use regression trees to build points typology of aircraft trajectories based on previous characteristics and to forecast crossing time of aircrafts on these points. The second model called amended CART is the previous model improved. This latter is built by replacing forecasting estimated by the mean of dependent variable inside the terminal nodes of classical CART by new forecasting given by multiple regression inside these nodes. This new model developed using Stepwise algorithm is parcimonious because for each terminal node it permits to explain the flight time by the most relevant predictors inside the node. The third model is built based on MARS (Multivariate adaptive regression splines) method. Besides continuity of the dependent variable estimator, this model allows to assess the direct and interaction effects of the explanatory variables on the crossing time on flight trajectory points. The fourth model uses boostrap sampling method. It’s random forests where for each bootstrap sample from the initial data, a tree regression model is built like in CART method. The general model forecasting is obtained by aggregating forecasting on the set of trees. Despite the overfitting observed on this model, it is robust and constitutes a solution against instability problem concerning regression trees obtained from CART method. The models we built have been assessed and validated using data test. Their using to compute the sector load forecasting in term to aircraft count entering the sector shown that, the forecast time horizon about 20 minutes with the interval time larger than 20 minutes, allowed to obtain forecasting with relative errors less than 10%. Among all these models, classical CART and random forests are more powerful. Hence, for regulator authority these models can be a very good help for managing the sector load of the airspace controlled.