Elements of Random Walk and Diffusion Processes

Author: Oliver C. Ibe
Publisher: John Wiley & Sons
ISBN: 1118617932
Format: PDF, ePub, Docs
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Presents an important and unique introduction to random walk theory Random walk is a stochastic process that has proven to be a useful model in understanding discrete-state discrete-time processes across a wide spectrum of scientific disciplines. Elements of Random Walk and Diffusion Processes provides an interdisciplinary approach by including numerous practical examples and exercises with real-world applications in operations research, economics, engineering, and physics. Featuring an introduction to powerful and general techniques that are used in the application of physical and dynamic processes, the book presents the connections between diffusion equations and random motion. Standard methods and applications of Brownian motion are addressed in addition to Levy motion, which has become popular in random searches in a variety of fields. The book also covers fractional calculus and introduces percolation theory and its relationship to diffusion processes. With a strong emphasis on the relationship between random walk theory and diffusion processes, Elements of Random Walk and Diffusion Processes features: Basic concepts in probability, an overview of stochastic and fractional processes, and elements of graph theory Numerous practical applications of random walk across various disciplines, including how to model stock prices and gambling, describe the statistical properties of genetic drift, and simplify the random movement of molecules in liquids and gases Examples of the real-world applicability of random walk such as node movement and node failure in wireless networking, the size of the Web in computer science, and polymers in physics Plentiful examples and exercises throughout that illustrate the solution of many practical problems Elements of Random Walk and Diffusion Processes is an ideal reference for researchers and professionals involved in operations research, economics, engineering, mathematics, and physics. The book is also an excellent textbook for upper-undergraduate and graduate level courses in probability and stochastic processes, stochastic models, random motion and Brownian theory, random walk theory, and diffusion process techniques.

Parameter Estimation in Fractional Diffusion Models

Author: Kęstutis Kubilius
Publisher: Springer
ISBN: 3319710303
Format: PDF, ePub
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This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.

Fractional Calculus

Author: Richard Herrmann
Publisher: World Scientific
ISBN: 9814551090
Format: PDF, ePub
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The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area. The contents are devoted to the application of fractional calculus to physical problems. The fractional concept is applied to subjects in classical mechanics, group theory, quantum mechanics, nuclear physics, hadron spectroscopy and quantum field theory and it will surprise the reader with new intriguing insights. This new, extended edition now also covers additional chapters about image processing, folded potentials in cluster physics, infrared spectroscopy and local aspects of fractional calculus. A new feature is exercises with elaborated solutions, which significantly supports a deeper understanding of general aspects of the theory. As a result, this book should also be useful as a supporting medium for teachers and courses devoted to this subject. Contents:IntroductionFunctionsThe Fractional DerivativeFriction ForcesFractional CalculusThe Fractional Harmonic OscillatorWave Equations and ParityNonlocality and Memory EffectsFractional Calculus in Multidimensional Space — 2D-Image ProcessingFractional Calculus in Multidimensional Space — 3D-Folded Potentials in Cluster PhysicsQuantum MechanicsThe Fractional Schrödinger Equation with the Infinite Well Potential — Numerical Results using the Riesz DerivativeUniqueness of a Fractional Derivative — the Riesz and Regularized Liouville Derivative as ExamplesFractional Spin — A Property of Particles Described with the Fractional Schrödinger EquationFactorizationSymmetriesThe Fractional Symmetric Rigid Rotorq-Deformed Lie Algebras and Fractional CalculusInfrared Spectroscopy of Diatomic Molecules Fractional Spectroscopy of HadronsMagic Numbers in Atomic NucleiMagic Numbers in Metal ClustersFractors — Fractional Tensor CalculusFractional FieldsGauge Invariance in Fractional Field TheoriesOn the Origin of SpaceOutlook Readership: Students and researchers in physics. Keywords:Mathematical Physics;Fractional Calculus;Long-Memory Kernels;Non-Local Field Theories;Fractional Quantum MechanicsKey Features:This was the first book on the market covering the full area of a physical application of fractional calculusThe book provides a skillful insight into a vividly growing research area and guides the reader from his first steps on an introductory level up to the current state of the art of a physical interpretation and application in different fieldsThis book enables the reader to participate and contribute to the development of this exciting research area by applying these methods in his own research area tooReviews:Reviews of the First Edition: “Fractional Calculus is an affordable and valuable introduction to the field that will appeal to physicists interested in scientific what-ifs.” Physics Today “… the first three chapters actually appear very helpful at the graduate level. Each chapter has a careful precis at the start. There a many analyses illustrating outcomes of fractional analyses… If this [fractional calculus] is the field of your research then this book is essential with numerous references… ” Contemporary Physics “The book has the property that derived results are directly compared with experimental findings. As a consequence, the reader is guided and encouraged to apply the fractional calculus approach in her/his research area. The reviewer strongly recommends this book for beginners as well as specialists in the fields of physics, mathematics and complex adaptive systems.” Zentralblatt MATH “A very welcome new feature in the second edition is the inclusion of exercises at the end of every chapter, with detailed solutions in the back of the book. This book is specifically aimed at physicists, although many of my colleagues outside physics have also found it useful. This is particularly true of graduate students and beginning researchers, or those new to the subject of fractional calculus.” Mark Meerschaert Dept of Statistics and Probability, Michigan State University

Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis

Author: Toshiyuki Sueyoshi
Publisher: John Wiley & Sons
ISBN: 1118979346
Format: PDF, ePub, Mobi
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Introduces a bold, new model for energy industry pollution prevention and sustainable growth Balancing industrial pollution prevention with economic growth is one of the knottiest problems faced by industry today. Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis introduces a novel approach to using data envelopment analysis (DEA) as a powerful tool for achieving that balance in the energy industries—the world's largest producers of greenhouse gases. It describes a rigorous framework that integrates elements of the social sciences, corporate strategy, regional economics, energy economics, and environmental policy, and delivers a methodology and a set of strategies for promoting green innovation while solving key managerial challenges to greenhouse gas reduction and business growth. In writing this book the authors have drawn upon their pioneering work and considerable experience in the field to develop an unconventional, holistic approach to using DEA to assess key aspects of sustainability development. The book is divided into two sections, the first of which lays out a conventional framework of DEA as the basis for new research directions. In the second section, the authors delve into conceptual and methodological extensions of conventional DEA for solving problems of environmental assessment in all contemporary energy industry sectors. Introduces a powerful new approach to using DEA to achieve pollution prevention, sustainability, and business growth Covers the fundamentals of DEA, including theory, statistical models, and practical issues of conventional applications of DEA Explores new statistical modeling strategies and explores their economic and business implications Examines applications of DEA to environmental analysis across the complete range of energy industries, including coal, petroleum, shale gas, nuclear energy, renewables, and more Summarizes important studies and nearly 800 peer reviewed articles on energy, the environment, and sustainability Environmental Assessment on Energy and Sustainability by Data Envelopment Analysis is a must-read for researchers, academics, graduate students, and practitioners in the energy industries, as well as government officials and policymakers tasked with regulating the environmental impacts of industrial pollution.

Brownian Motion Calculus

Author: Ubbo F. Wiersema
Publisher: John Wiley & Sons
ISBN: 0470021713
Format: PDF, ePub, Docs
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Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website.

The Mathematics of Diffusion

Author: John Crank
Publisher: Oxford University Press
ISBN: 9780198534112
Format: PDF, Kindle
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Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.

Principles of Forecasting

Author: J. S. Armstrong
Publisher: Springer Science & Business Media
ISBN: 9780792379300
Format: PDF, Kindle
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This work summarizes knowledge from experts and from empirical studies, providing guidelines that can be applied in fields such as economics, sociology, and psychology. The 30 chapters cover various forecsating methods, from judgemental to quantitative.

Game Theory

Author: E. N. Barron
Publisher: John Wiley & Sons
ISBN: 1118216938
Format: PDF
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This text confirms the role of mathematics in making logical and advantageous decisions and uses modern software applications to create, analyse, and implement effective decision-making models