LEADER 05681nam 2200733Ia 450 001 9910784594003321 005 20200520144314.0 010 $a1-281-00388-3 010 $a9786611003883 010 $a0-08-047536-1 035 $a(CKB)1000000000357687 035 $a(EBL)291692 035 $a(OCoLC)162131511 035 $a(SSID)ssj0000251583 035 $a(PQKBManifestationID)11227648 035 $a(PQKBTitleCode)TC0000251583 035 $a(PQKBWorkID)10175278 035 $a(PQKB)10347338 035 $a(Au-PeEL)EBL291692 035 $a(CaPaEBR)ebr10172768 035 $a(CaONFJC)MIL100388 035 $z(PPN)151034877 035 $a(MiAaPQ)EBC291692 035 $a(PPN)170240908 035 $a(EXLCZ)991000000000357687 100 $a20070123d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic processes in physics and chemistry$b[electronic resource] /$fN.G. van Kampen 205 $a3rd ed. 210 $aAmsterdam ;$aLondon $cElsevier$d2007 215 $a1 online resource (481 p.) 225 1 $aNorth-Holland personal library 300 $aPrevious ed.: Amsterdam: North-Holland, 1992. 311 $a0-444-52965-9 320 $aIncludes bibliographical references and index. 327 $aFront Cover; Stochastic Processes in Physics and Chemistry; Copyright Page; PREFACE TO THE FIRST EDITION; PREFACE TO THE SECOND EDITION; ABBREVIATED REFERENCES; PREFACE TO THE THIRD EDITION; TABLE OF CONTENTS; Chapter I. STOCHASTIC VARIABLES; 1. Definition; 2. Averages; 3. Multivariate distributions; 4. Addition of stochastic variables; 5. Transformation of variables; 6. The Gaussian distribution; 7. The central limit theorem; Chapter II. RANDOM EVENTS; 1. Definition; 2. The Poisson distribution; 3. Alternative description of random events; 4. The inverse formula; 5. The correlation functions 327 $a6. Waiting times7. Factorial correlation functions; Chapter III. STOCHASTIC PROCESSES; 1. Definition; 2. Stochastic processes in physics; 3. Fourier transformation of stationary processes; 4. The hierarchy of distribution functions; 5. The vibrating string and random fields; 6. Branching processes; Chapter IV. MARKOV PROCESSES; 1. The Markov property; 2. The Chapman-Kolmogorov equation; 3. Stationary Markov processes; 4. The extraction of a subensemble; 5. Markov chains; 6. The decay process; Chapter V. THE MASTER EQUATION; 1. Derivation; 2. The class of W-matrices; 3. The long-time limit 327 $a4. Closed, isolated, physical systems5. The increase of entropy; 6. Proof of detailed balance; 7. Expansion in eigenfunctions; 8. The macroscopic equation; 9. The adjoint equation; 10. Other equations related to the master equation; Chapter VI. ONE-STEP PROCESSES; 1. Definition; the Poisson process; 2. Random walk with continuous time; 3. General properties of one-step processes; 4. Examples of linear one-step processes; 5. Natural boundaries; 6. Solution of linear one-step processes with natural boundaries; 7. Artificial boundaries; 8. Artificial boundaries and normal modes 327 $a9. Nonlinear one-step processesChapter VII. CHEMICAL REACTIONS; 1. Kinematics of chemical reactions; 2. Dynamics of chemical reactions; 3. The stationary solution; 4. Open systems; 5. Unimolecular reactions; 6. Collective systems; 7. Composite Markov processes; Chapter VIII. THE FOKKER-PLANCK EQUATION; 1. Introduction; 2. Derivation of the Fokker-Planck equation; 3. Brownian motion; 4. The Rayleigh particle; 5. Application to one-step processes; 6. The multivariate Fokker-PIanck equation; 7. Kramers' equation; Chapter IX. THE LANGEVIN APPROACH; 1. Langevin treatment of Brownian motion 327 $a2. Applications3. Relation to Fokker-Planck equation; 4. The Langevin approach; 5. Discussion of the Ito?-Stratonovich dilemma; 6. Non-Gaussian white noise; 7. Colored noise; Chapter X. THE EXPANSION OF THE MASTER EQUATION; 1. Introduction to the expansion; 2. General formulation of the expansion method; 3. The emergence of the macroscopic law; 4. The linear noise approximation; 5. Expansion of a multivariate master equation; 6. Higher orders; Chapter XI. THE DIFFUSION TYPE; 1. Master equations of diffusion type; 2. Diffusion in an external field; 3. Diffusion in an inhomogeneous medium 327 $a4. Muitivariate diffusion equation 330 $aThe third edition of Van Kampen's standard work has been revised and updated. The main difference with the second edition is that the contrived application of the quantum master equation in section 6 of chapter XVII has been replaced with a satisfactory treatment of quantum fluctuations. Apart from that throughout the text corrections have been made and a number of references to later developments have been included. From the recent textbooks the following are the most relevant. C.W.Gardiner, Quantum Optics (Springer, Berlin 1991)D.T. Gillespie, Markov Processes (Academic Press, Sa 410 0$aNorth-Holland personal library. 606 $aStochastic processes 606 $aStatistical physics 606 $aChemistry, Physical and theoretical$xStatistical methods 615 0$aStochastic processes. 615 0$aStatistical physics. 615 0$aChemistry, Physical and theoretical$xStatistical methods. 676 $a519.202453 686 $a33.26$2bcl 686 $a35.05$2bcl 700 $aKampen$b N. G. van$020957 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784594003321 996 $aStochastic processes in physics and chemistry$9336408 997 $aUNINA