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This book introduces random currents by presenting underlying mathematical methods necessary for applications. The theory of currents is an advanced topic in geometric measure theory that extends distribution to linear functionals within the space of differential forms of any order. Methods to extend random distributions to random currents are introduced and analyzed in this book. Beginning with an overview of mathematical aspects of the theory of currents, this book moves on to examine applications in medicine, material science, and image analysis. Applied researchers will find the practical modern mathematical methods along with the detailed appendix useful to stimulate new applications and research. .

Stochastic processes. --- Random processes --- Probabilities --- Mathematics. --- Computer vision. --- Distribution (Probability theory. --- Measure and Integration. --- Image Processing and Computer Vision. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Math --- Science --- Measure theory. --- Optical data processing. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Optical equipment

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This book introduces random currents by presenting underlying mathematical methods necessary for applications. The theory of currents is an advanced topic in geometric measure theory that extends distribution to linear functionals within the space of differential forms of any order. Methods to extend random distributions to random currents are introduced and analyzed in this book. Beginning with an overview of mathematical aspects of the theory of currents, this book moves on to examine applications in medicine, material science, and image analysis. Applied researchers will find the practical modern mathematical methods along with the detailed appendix useful to stimulate new applications and research. .

Operational research. Game theory --- Probability theory --- Mathematics --- Mathematical physics --- Computer. Automation --- computervisie --- beeldverwerking --- differentiaalvergelijkingen --- waarschijnlijkheidstheorie --- stochastische analyse --- wiskunde --- kansrekening

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This book consists of lecture notes of a summer school named after the late Jacques Louis Lions. The summer school was designed to alert both Academia and Industry to the increasing role of multidisciplinary methods and tools for the design of complex products in various areas of socio-economic intereSt. This volume offers the reader a rare opportunity of being exposed to the presentation of real industrial and societal problems together with the relevant innovative methods used.

Mathematical optimization. --- Mathematical analysis. --- Multidisciplinary design optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Design optimization, Multidisciplinary --- Multicriteria design optimization --- Multidisciplinary optimization (Engineering design) --- Combinatorial optimization --- Engineering design --- 517.1 Mathematical analysis --- Differential equations, partial. --- Computer science --- Engineering mathematics. --- Hydraulic engineering. --- Vibration. --- Partial Differential Equations. --- Optimization. --- Computational Mathematics and Numerical Analysis. --- Mathematical and Computational Engineering. --- Engineering Fluid Dynamics. --- Vibration, Dynamical Systems, Control. --- Mathematics. --- Cycles --- Mechanics --- Sound --- Partial differential equations --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Engineering analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Partial differential equations. --- Computer mathematics. --- Applied mathematics. --- Fluid mechanics. --- Dynamical systems. --- Dynamics. --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Hydromechanics --- Continuum mechanics

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From reviews of First Edition: The book is ... an account of fundamental concepts as they appear in relevant modern applications and literature. ... The book addresses three main groups: first, mathematicians working in a different field; second, other scientists and professionals from a business or academic background; third, graduate or advanced undergraduate students of a quantitative subject related to stochastic theory and/or applications. —Zentralblatt MATH This is an introductory text on continuous time stochastic processes and their applications to finance and biology. ... The book will be useful for applied mathematicians who are not probabilists to get a quick flavour of the techniques of stochastic calculus, and for professional probabilists to get a quick flavour of the applications. —Mathematical Reviews Revised and enhanced, this concisely written second edition of An Introduction to Continuous-Time Stochastic Processes is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic  integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics include: * Markov processes * Stochastic differential equations * Arbitrage-free markets and financial derivatives * Insurance risk * Population dynamics * Agent-based models New to the Second Edition: * Improved presentation of original concepts * Expanded background on probability theory * Substantial material applicable to finance and biology, including stable laws, Lévy processes, and Itô-Lévy calculus * Supplemental appendix to provide basic facts on semigroups of linear operators An Introduction to Continuous-Time Stochastic Processes, Second Edition will be of interest to a broad audience of students, pure and applied mathematicians, and researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering. Suitable as a textbook for graduate or undergraduate courses, as well as European Masters courses (according to the two-year-long second cycle of the “Bologna Scheme”), the work may also be used for self-study or as a reference. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided.

Finance. --- Mathematical optimization. --- Models, Theoretical. --- Stochastic processes. --- Stochastic processes --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Probabilities. --- Probability --- Statistical inference --- Random processes --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Economics, Mathematical. --- Mathematical models. --- Biomathematics. --- Probability Theory and Stochastic Processes. --- Mathematical Modeling and Industrial Mathematics. --- Quantitative Finance. --- Mathematical and Computational Biology. --- Applications of Mathematics. --- Appl.Mathematics/Computational Methods of Engineering. --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Probabilities --- Distribution (Probability theory. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Mathematical analysis --- Math --- Science --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Economics, Mathematical . --- Biology --- Mathematical economics --- Econometrics --- Models, Mathematical --- Simulation methods --- Methodology --- Social sciences --- Probability Theory. --- Mathematics in Business, Economics and Finance. --- Mathematical and Computational Engineering Applications. --- Data processing.

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This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields. Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations. An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularly the applications explored in the second half of the book.

Stochastic processes --- Mathematical models. --- Processos estocàstics --- Models matemàtics --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Mètodes de simulació --- Anàlisi de sistemes --- Mètode de Montecarlo --- Modelització multiescala --- Models economètrics --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Programació (Ordinadors) --- Simulació per ordinador --- Teoria de màquines --- Models biològics --- Càlcul estocàstic --- Funcions aleatòries --- Processos aleatoris --- Probabilitats --- Anàlisi estocàstica --- Aproximació estocàstica --- Camps aleatoris --- Filtre de Kalman --- Fluctuacions (Física) --- Martingales (Matemàtica) --- Processos de Markov --- Processos de ramificació --- Processos gaussians --- Processos puntuals --- Rutes aleatòries (Matemàtica) --- Semimartingales (Matemàtica) --- Sistemes estocàstics --- Teoremes de límit (Teoria de probabilitats) --- Teoria de cues --- Teoria de l'estimació --- Teoria de la predicció --- Stochastic processes. --- Stochastic models. --- Social sciences --- Biomathematics. --- Stochastic Processes. --- Stochastic Modelling. --- Mathematical Modeling and Industrial Mathematics. --- Mathematics in Business, Economics and Finance. --- Mathematical and Computational Biology. --- Mathematics. --- Biology --- Mathematics --- Models, Mathematical --- Simulation methods --- Models, Stochastic --- Mathematical models --- Random processes --- Probabilities