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Markov Processes

Author: Daniel T. Gillespie
Publisher: Gulf Professional Publishing
ISBN: 9780122839559
Size: 50.17 MB
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Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level. A self-contained, prgamatic exposition of the needed elements of random variable theory Logically integrated derviations of the Chapman-Kolmogorov equation, the Kramers-Moyal equations, the Fokker-Planck equations, the Langevin equation, the master equations, and the moment equations Detailed exposition of Monte Carlo simulation methods, with plots of many numerical examples Clear treatments of first passages, first exits, and stable state fluctuations and transitions Carefully drawn applications to Brownian motion, molecular diffusion, and chemical kinetics

An Introduction To Stochastic Processes In Physics

Author: Don S. Lemons
Publisher: JHU Press
ISBN: 9780801868672
Size: 60.74 MB
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"Students will love this book. It tells them without fuss how to do simple and useful numerical calculations, with just enough background to understand what they are doing... a refreshingly brief and unconvoluted work." -- American Journal of Physics

An Introduction To Stochastic Processes With Applications To Biology Second Edition

Author: Linda J. S. Allen
Publisher: CRC Press
ISBN: 143989468X
Size: 78.97 MB
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An Introduction to Stochastic Processes with Applications to Biology, Second Edition presents the basic theory of stochastic processes necessary in understanding and applying stochastic methods to biological problems in areas such as population growth and extinction, drug kinetics, two-species competition and predation, the spread of epidemics, and the genetics of inbreeding. Because of their rich structure, the text focuses on discrete and continuous time Markov chains and continuous time and state Markov processes. New to the Second Edition A new chapter on stochastic differential equations that extends the basic theory to multivariate processes, including multivariate forward and backward Kolmogorov differential equations and the multivariate Itô’s formula The inclusion of examples and exercises from cellular and molecular biology Double the number of exercises and MATLAB® programs at the end of each chapter Answers and hints to selected exercises in the appendix Additional references from the literature This edition continues to provide an excellent introduction to the fundamental theory of stochastic processes, along with a wide range of applications from the biological sciences. To better visualize the dynamics of stochastic processes, MATLAB programs are provided in the chapter appendices.

Diffusion

Author: Sushanta Dattagupta
Publisher: Taylor & Francis
ISBN: 1439895570
Size: 14.95 MB
Format: PDF
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Within a unifying framework, Diffusion: Formalism and Applications covers both classical and quantum domains, along with numerous applications. The author explores the more than two centuries-old history of diffusion, expertly weaving together a variety of topics from physics, mathematics, chemistry, and biology. The book examines the two distinct paradigms of diffusion—physical and stochastic—introduced by Fourier and Laplace and later unified by Einstein in his groundbreaking work on Brownian motion. The author describes the role of diffusion in probability theory and stochastic calculus and discusses topics in materials science and metallurgy, such as defect-diffusion, radiation damage, and spinodal decomposition. In addition, he addresses the impact of translational/rotational diffusion on experimental data and covers reaction-diffusion equations in biology. Focusing on diffusion in the quantum domain, the book also investigates dissipative tunneling, Landau diamagnetism, coherence-to-decoherence transition, quantum information processes, and electron localization.

Stochastic Processes In Physics And Chemistry

Author: N.G. Van Kampen
Publisher: Elsevier
ISBN: 9780080475363
Size: 38.44 MB
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The third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant. C.W.Gardiner, Quantum Optics (Springer, Berlin 1991) D.T. Gillespie, Markov Processes (Academic Press, San Diego 1992) W.T. Coffey, Yu.P.Kalmykov, and J.T.Waldron, The Langevin Equation (2nd edition, World Scientific, 2004) * Comprehensive coverage of fluctuations and stochastic methods for describing them * A must for students and researchers in applied mathematics, physics and physical chemistry

Introduction To Stochastic Analysis

Author: Vigirdas Mackevicius
Publisher: John Wiley & Sons
ISBN: 1118603249
Size: 64.96 MB
Format: PDF, Kindle
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This is an introduction to stochastic integration and stochasticdifferential equations written in an understandable way for a wideaudience, from students of mathematics to practitioners in biology,chemistry, physics, and finances. The presentation is based on thenaïve stochastic integration, rather than on abstract theoriesof measure and stochastic processes. The proofs are rather simplefor practitioners and, at the same time, rather rigorous formathematicians. Detailed application examples in natural sciencesand finance are presented. Much attention is paid to simulationdiffusion processes. The topics covered include Brownian motion; motivation ofstochastic models with Brownian motion; Itô and Stratonovichstochastic integrals, Itô’s formula; stochasticdifferential equations (SDEs); solutions of SDEs as Markovprocesses; application examples in physical sciences and finance;simulation of solutions of SDEs (strong and weak approximations).Exercises with hints and/or solutions are also provided.

Applied Probability And Stochastic Processes

Author: Michel K. Ochi
Publisher: Wiley-Interscience
ISBN:
Size: 46.75 MB
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This introduction to modern concepts of applied stochastic processes is written for a broad range of applications in diverse areas of engineering and the physical sciences (unlike other books, which are written primarily for communications or electrical engineering). Emphasis is on clarifying the basic principles supporting current prediction techniques. The first eight chapters present the probability theory relevant to analysis of stochastic processes. The following nine chapters discuss principles, advanced techniques (including the procedures of spectral analysis and the development of the probability density function) and applications. Also features material found in the recent literature such as higher-order spectral analysis, the joint probability distribution of amplitudes and periods and non-Gaussian random processes. Includes numerous illustrative examples.

Simple Brownian Diffusion

Author: Daniel Thomas Gillespie
Publisher: Oxford University Press
ISBN: 0199664501
Size: 54.99 MB
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Brownian diffusion, the motion of large molecules in a sea of very many much smaller molecules, is topical because it is one of the ways in which biologically important molecules move about inside living cells. This book presents the mathematical physics that underlies the four simplest models of Brownian diffusion.

Enzyme Kinetics Catalysis And Control

Author: Daniel L. Purich
Publisher: Elsevier
ISBN: 0123809258
Size: 49.55 MB
Format: PDF
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Far more than a comprehensive treatise on initial-rate and fast-reaction kinetics, this one-of-a-kind desk reference places enzyme science in the fuller context of the organic, inorganic, and physical chemical processes occurring within enzyme active sites. Drawing on 2600 references, Enzyme Kinetics: Catalysis & Control develops all the kinetic tools needed to define enzyme catalysis, spanning the entire spectrum (from the basics of chemical kinetics and practical advice on rate measurement, to the very latest work on single-molecule kinetics and mechanoenzyme force generation), while also focusing on the persuasive power of kinetic isotope effects, the design of high-potency drugs, and the behavior of regulatory enzymes. Historical analysis of kinetic principles including advanced enzyme science Provides both theoretical and practical measurements tools Coverage of single molecular kinetics Examination of force generation mechanisms Discussion of organic and inorganic enzyme reactions

An Introduction To Information Theory

Author: Fazlollah M. Reza
Publisher: Courier Corporation
ISBN: 0486158446
Size: 37.80 MB
Format: PDF, ePub, Mobi
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Graduate-level study for engineering students presents elements of modern probability theory, information theory, coding theory, more. Emphasis on sample space, random variables, capacity, etc. Many reference tables and extensive bibliography. 1961 edition.