Screen LibraryMarkov processes : an introduction for physical scientists /
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...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
Academic Press,
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| Publisher Address: | Boston : |
| Publication Dates: | 1992. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/book/9780122839559 |
| Summary: |
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. Key Features * 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. |
| Carrier Form: | 1 online resource (xxi, 565 pages) : illustrations |
| Bibliography: | Includes bibliographical references (page xxi) and index. |
| ISBN: |
9780080918372 0080918379 1299536166 9781299536166 |
| Index Number: | QA274 |
| CLC: | O211.62 |
| Contents: |
Front Cover; Markov Processes: An Introducation for Pshysical Science; Copyright Page; Table of Contents; Preface; Acknowledgments; Bibliography; Chapter 1. Random Variable Theory; 1.1 The laws of probability; 1.2 Definition of a random variable; 1.3 Averages and moments; 1.4 Four important random variables; 1.5 Joint random variables; 1.6 Some useful theorems; 1.7 Integer random variables; 1.8 Random number generating procedures; Chapter 2. General Features of a Markov Process; 2.1 The Markov state density function; 2.2 The Chapman-Kolmogorov equation. 2.3 Functions of state and their averages2.4 The Markov propagator; 2.5 The Kramers-Moyal equations; 2.6 The time-integral of a Markov process; 2.7 Time-evolution of the moments; 2.8 Homogeneity; 2.9 The Monte Carlo approach; Chapter 3. Continuous Markov Processes; 3.1 The continuous propagator and its characterizing functions; 3.2 Time-evolution equations; 3.3 Three important continuous Markov processes; 3.4 The Lange vin equation; 3.5 Stable processes; 3.6 Some examples of stable processes; 3.7 First exit time theory; 3.8 Weak noise processes. 3.9 Monte Carlo simulation of continuous Markov processesChapter 4. Jump Markov Processes with Continuum States; 4.1 The jump propagator and its characterizing functions; 4.2 Time-evolution equations; 4.3 The next-jump density function; 4.4 Completely homogeneous jump Markov processes; 4.5 A rigorous approach to self-diffusion and Brownian motion; 4.6 Monte Carlo simulation of continuum-state jump Markov processes; Chapter 5. Jump Markov Processes with Discrete States; 5.1 Foundational elements of discrete state Markov processes; 5.2 Completely homogeneous discrete state processes. 5.3 Temporally homogeneous Markov processes on the nonnegative integersChapter 6. Temporally Homogeneous Birth-Death Markov Processes; 6.1 Foundational elements; 6.2 The continuous approximation for birth-death Markov processes; 6.3 Some simple birth-death Markov processes; 6.4 Stable birth-death Markov processes; 6.5 Application: The fundamental postulate of statistical; 6.6 The first passage time; 6.7 First exit from an interval; 6.8 Stable state fluctuations and transitions; Appendix A: Some Useful Integral Identities; Appendix B: Integral Representations of the Delta Functions. Appendix C: An Approximate Solution Procedure for ""Open"" Moment Evolution EquationsAppendix D: Estimating the Width and Area of a Function Peak; Appendix E: Can the Accuracy of the Continuous Process Simulation Formula Be Improved?; Appendix F: Proof of the Birth-death Stability Theorem; Appendix G: Solution of the Matrix Differential Equation (6.6-62); Index. |