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Markov 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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boston :
Academic Press,
�1992.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Gillespie, Daniel T. | |
| 245 | 1 | 0 | |a Markov processes : |b an introduction for physical scientists / |c Daniel T. Gillespie. |
| 260 | |a Boston : |b Academic Press, |c �1992. | ||
| 300 | |a 1 online resource (xxi, 565 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 504 | |a Includes bibliographical references (page xxi) and index. | ||
| 520 | |a 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. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Front Cover; Markov Processes: An Introduction 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 546 | |a English. | ||
| 650 | 0 | |a Markov processes. | |
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| 776 | 0 | 8 | |i Print version: |a Gillespie, Daniel T. |t Markov processes. |d Boston : Academic Press, �1992 |z 0122839552 |w (DLC) 91025738 |w (OCoLC)24064770 |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780122839559 |z Texto completo |