1,720,992 research outputs found
Monotonicity properties of multi-dimensional reflected diffusions in random environment and applications
No full textWe consider an N-dimensional reflected process, modeling an infinite capacity fluid queues network, of which service and input rates depend on the queue levels as well as on the state of an exterior ergodic stationary process. N is the number of queues in the network. We prove a monotonicity result for such a process, from which we deduce stability results for networks of queues. Particular attention is paid to the case N=2. Next, we give some applications of those stability results.Fluid queues Stochastic networks Reflected stochastic differential equation
Monotonicity properties of multi-dimensional reflected diffusions in random environment and application
No full textInternational audienceWe consider an N-dimensional reflected process, modeling an infinite capacity fluid queues network, of which service and input rates depend on the queue levels as well as on the state of an exterior ergodic stationary process. N is the number of queues in the network. We prove a monotonicity result for such a process, from which we deduce stability results for networks of queues. Particular attention is paid to the case N=2. Next, we give some applications of those stability results
Asymptotics for infinite server queues with fast/slow Markov switching and fat tailed service times
No full textWe study a general dimensional infinite server queues process with Markov switching, Poisson arrivals and where the service times are fat tailed with index . When the arrival rate is sped up by a factor , the transition probabilities of the underlying Markov chain are divided by and the service times are divided by , we identify two regimes ("fast arrivals", when , and "equilibrium", when ) in which we prove that a properly rescaled process converges pointwise in distribution to some limiting process. In a third "slow arrivals" regime, , we show the convergence of the two first joint moments of the rescaled process
Contribution à quelques problèmes de premier passage et de ruine multidimensionnels: Lien avec les réseaux de files fluides
Get PDFRisk processes with interest force in Markovian environment
No full textInternational audienceWe consider risk processes modulated by an external Markov chain, with claim amounts following phase-type distributions, featuring an interest rate factor. We are interested in the distribution of exit times, which we study through proper transformations of the original processes, through duality and Markovian embeddings. In dimension 1, this corresponds to the classic ruin time of which we compute the distribution. We also consider K dimensional processes, of which exits out of quadrants are studied
Moments of a Markov-modulated, irreducible network of fluid queues.
No full textInternational audienceWe study a network of fluid queues in which exogenous arrivals are modulated by a continuous-time Markov chain. Service rates in each queue are proportional to the queue size, and the network is assumed to be irreducible. The queue levels satisfy a linear, vector-valued differential equation. We obtain joint moments of the queue sizes recursively, and deduce the Laplace transform of the queue sizes in the stationary regime
A Markov additive risk process in dimension 2 perturbed by a fractional Brownian motion
No full textAbstractWe consider the following theoretical reinsurance ruin problem. An insurance company has two types of independent claims, respectively modeled by a Markov additive process (large claims) and a fractional Brownian motion (small claims) with Hurst parameter H∈[1/2,1), and chooses to reinsure both of them according to a quota share policy. This leads to studying a bivariate risk process. We study two types of ruins, corresponding to either ruin of one of the risk processes, or of both. We obtain asymptotics of the corresponding ruin probabilities when initial reserves tend to infinity along a direction
Decision-making processes in civil aviation using incident reports and flight data records for precursors detection and weak signals
No full textL’approche présentée par cette thèse, est en effet une stratégie proactive pour anticiper la détectiondes signaux faibles et précurseurs, mais aussi une approche « corporative », grâce à laquelle la miseen œuvre de marqueurs est pertinente et s’appuie sur un surcroît de retour d'expériences et deréelles « best practices », qui sont de plus en plus surveillées.La thèse aborde des questions spécifiques liées à l'analyse des données appliquées à l'aviation civile,par la modélisation des paramètres de vol provenant de l'enregistreur à accès rapide (QAR). L'études'est concentrée sur trois aspects : (1) la compréhension des opérations aériennes, del'environnement de la maintenance et du système de collecte des données ; (2) l'étude desmodélisations statistiques dans le but d'identifier les « signaux annonciateurs » pertinents pour lagestion de la santé des aéronefs ; et (3) la définition des seuils capables de traiter non seulement, lessituations critiques, mais également de détecter et de hiérarchiser les modules de diagnostic. Unearchitecture pour la gestion et l'exploration des données de maintenance aéronautique et l'utilisationdes résultats pour mettre à jour les modèlesThe operations of aircraft fleets typically result in large volumes of data collected duringthe execution of various operational and support processes. The thesis addresses specificissues related to the data analysis applied in civil aviation, by analysing and modellingflight data parameters from the quick accesses recorder (QAR). The study focused onthree aspects: (1) understanding the aviation operations, maintenance environment, anddata collection system; (2) investigating data analysis approaches with the purpose ofidentifying promising methods pertinent to aircraft health management; and (3) definingrequirements for a tool to support the aviation maintenance planners and fleet managers.Results of preliminary analyses of two maintenance data and flight data sets arepresented. An architecture for managing and mining aviation maintenance data and usingresults to update models used by diagnostic modules for fault isolation duringmaintenance activity is also presented
High order expansions for renewal functions and applications to ruin theory
No full textInternational audienceA high order expansion of the renewal function is provided under the assumption that the inter-renewal time distribution is light tailed with finite moment generating function g on a neighborhood of 0. This expansion relies on complex analysis and is expressed in terms of the residues of the function 1/(1 − g). Under the assumption that g can be extended into a meromorphic function on the complex plane and some technical conditions , we obtain even an exact expansion of the renewal function. An application to risk theory is given where we consider high order expansion of the ruin probability for the standard compound Poisson risk model. This precises the well known Crámer-Lundberg approximation of the ruin probability when the initial reserve is large
Stability analysis of second-order fluid flow models in a stationary ergodic environment
No full textInternational audienc
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