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Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes. The emphasis of this book is on special classes of such Brownian functionals as: - Gaussian subspaces of the Gaussian space of Brownian motion; - Brownian quadratic functionals; - Brownian local times, - Exponential functionals of Brownian motion with drift; - Winding number of one or several Brownian motions around one or several points or a straight line, or curves; - Time spent by Brownian motion below a multiple of its one-sided supremum. Besides its obvious audience of students and lecturers the book also addresses the interests of researchers from core probability theory out to applied fields such as polymer physics and mathematical finance.

Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Math --- Science --- Brownian motion processes. --- Potential theory (Mathematics) --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Wiener processes --- Brownian movements --- Fluctuations (Physics) --- Markov processes --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Distribution (Probability theory)

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Biomedical imaging is a fascinating research area to applied mathematicians. Challenging imaging problems arise and they often trigger the investigation of fundamental problems in various branches of mathematics. This is the first book to highlight the most recent mathematical developments in emerging biomedical imaging techniques. The main focus is on emerging multi-physics and multi-scales imaging approaches. For such promising techniques, it provides the basic mathematical concepts and tools for image reconstruction. Further improvements in these exciting imaging techniques require continued research in the mathematical sciences, a field that has contributed greatly to biomedical imaging and will continue to do so. The volume is suitable for a graduate-level course in applied mathematics and helps prepare the reader for a deeper understanding of research areas in biomedical imaging.

Diagnostic imaging --- Biomedical engineering --- Mathematics. --- Clinical imaging --- Imaging, Diagnostic --- Medical diagnostic imaging --- Medical imaging --- Noninvasive medical imaging --- Diagnosis, Noninvasive --- Imaging systems in medicine --- Clinical engineering --- Medical engineering --- Bioengineering --- Biophysics --- Engineering --- Medicine --- Internal medicine. --- Potential theory (Mathematics). --- Differential equations, partial. --- Differential Equations. --- Internal Medicine. --- Mathematical and Computational Biology. --- Potential Theory. --- Partial Differential Equations. --- Ordinary Differential Equations. --- 517.91 Differential equations --- Differential equations --- Partial differential equations --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Medicine, Internal --- Biomathematics. --- Partial differential equations. --- Differential equations. --- Biology --- Mathematics

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This volume contains the revised and completed notes of lectures given at the school "Quantum Potential Theory: Structure and Applications to Physics," held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald from February 26 to March 10, 2007. Quantum potential theory studies noncommutative (or quantum) analogs of classical potential theory. These lectures provide an introduction to this theory, concentrating on probabilistic potential theory and it quantum analogs, i.e. quantum Markov processes and semigroups, quantum random walks, Dirichlet forms on C* and von Neumann algebras, and boundary theory. Applications to quantum physics, in particular the filtering problem in quantum optics, are also presented.

Potential theory (Mathematics) --- Markov processes. --- Semigroups. --- Functional analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Group theory --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Global analysis. --- Quantum theory. --- Global differential geometry. --- Potential theory (Mathematics). --- Global Analysis and Analysis on Manifolds. --- Quantum Physics. --- Quantum Information Technology, Spintronics. --- Differential Geometry. --- Potential Theory. --- Global analysis (Mathematics) --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Geometry, Differential --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Thermodynamics --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Quantum physics. --- Quantum computers. --- Spintronics. --- Differential geometry. --- Differential geometry --- Fluxtronics --- Magnetoelectronics --- Spin electronics --- Spinelectronics --- Microelectronics --- Nanotechnology --- Computers --- Topology --- Greifswald <2007>