This volume is based on the lecture notes of six courses delivered at a CIMPA Summer School in Temuco, Chile, in January 2001. The courses are: asymptotic of the heat kernel in unbounded domains; spin systems with long range interactions; non-linear Dirichlet problem and non-linear integration; first-passage percolation; central limit theorem for Markov processes; stochastic orders and stopping times in Brownian motion. The level of each course is that of a graduate course, but the material will also be of interest for the specialist.
This volume is based on the lecture notes of six courses delivered at a CIMPA Summer School in Temuco, Chile, in January 2001. The courses are: asymptotic of the heat kernel in unbounded domains; spin systems with long range interactions; non-linear Dirichlet problem and non-linear integration; first-passage percolation; central limit theorem for Markov processes; stochastic orders and stopping times in Brownian motion. The level of each course is that of a graduate course, but the material will also be of interest for the specialist.
Main concepts of quasi-stationary distributions (QSDs) for killed processes are the focus of the present volume. For diffusions, the killing is at the boundary and for dynamical systems there is a trap. The authors present the QSDs as the ones that allow describing the long-term behavior conditioned to not being killed. Studies in this research area started with Kolmogorov and Yaglom and in the last few decades have received a great deal of attention. The authors provide the exponential distribution property of the killing time for QSDs, present the more general result on their existence and study the process of trajectories that survive forever. For birth-and-death chains and diffusions, the existence of a single or a continuum of QSDs is described. They study the convergence to the extremal QSD and give the classification of the survival process. In this monograph, the authors discuss Gibbs QSDs for symbolic systems and absolutely continuous QSDs for repellers. The findings described are relevant to researchers in the fields of Markov chains, diffusions, potential theory, dynamical systems, and in areas where extinction is a central concept. The theory is illustrated with numerous examples. The volume uniquely presents the distribution behavior of individuals who survive in a decaying population for a very long time. It also provides the background for applications in mathematical ecology, statistical physics, computer sciences, and economics.
Pierre Coulibeuf est cinéaste et plasticien. À partir de 1987, il réalise des fictions expérimentales qui investissent savamment le champ de l'art, et dans lesquelles les changements d'identité, le dédoublement, la métamorphose affectent les univers et les artistes qui inspirent ses oeuvres. Dans ce catalogue, l'artiste décrit un monde fait de " signes obscurs, de figures mouvantes, étranges ", un monde devenu fable. Les diverses réalités de l'art : peinture, photographie, cinéma, littérature, musique ou danse, sont impliquées dans ses oeuvres, en particulier dans Dédale (2009), film- installation composé de quatre images en mouvement et d'une série de photographies (commande de la Fondation Iberê Camargo, Porto Alegre, Brésil). " La dynamique mentale qui innerve l'oeuvre filmique recomposée dans l'espace d'exposition met les réalités de l'art en mouvement, brouille les codes et les frontières, suscite une réalité autre, instable, ouverte à l'activité combinatoire du regardeur " (P Coulibeuf).
This book presents the first comprehensive and modern mathematical treatment of these mean field particle models, including refined convergence analysis on nonlinear Markov chain models. It also covers applications related to parameter estimation in hidden Markov chain models, stochastic optimization, nonlinear filtering and multiple target tracking, stochastic optimization, calibration and uncertainty propagations in numerical codes, rare event simulation, financial mathematics, and free energy and quasi-invariant measures arising in computational physics and population biology.
The book is devoted to the very basis of acoustics and vibro-acoustics. The physics of the phenomena, the analytical methods and the modern numerical techniques are presented in a concise form. Many examples illustrate the fundamental problems and predictions (analytic or numerical) and are often compared to experiments. Some emphasis is put on the mathematical tools required by rigorous theory and reliable prediction methods. A series of practical problems, which reflect the content of each chapter Reference to the major treatises and fundamental recent papers Current computing techniques, used in problem solving
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