LEADER 06069nam 2200841Ia 450 001 9910139764203321 005 20200520144314.0 010 $a1-282-27959-9 010 $a9786612279591 010 $a3-527-62609-3 010 $a3-527-62610-7 035 $a(CKB)1000000000789883 035 $a(EBL)481407 035 $a(OCoLC)587404596 035 $a(SSID)ssj0000354635 035 $a(PQKBManifestationID)11965144 035 $a(PQKBTitleCode)TC0000354635 035 $a(PQKBWorkID)10302563 035 $a(PQKB)10767469 035 $a(MiAaPQ)EBC481407 035 $a(Au-PeEL)EBL481407 035 $a(CaPaEBR)ebr10333009 035 $a(CaONFJC)MIL227959 035 $a(MiAaPQ)EBC7104662 035 $a(Au-PeEL)EBL7104662 035 $a(JP-MeL)3000110934 035 $a(EXLCZ)991000000000789883 100 $a20140717d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPhysics of stochastic processes $ehow randomness acts in time /$fby Reinhard Mahnke, Jevgenijs Kaupuzs, Ihor Lubashevsky 210 $aWeinheim $cWiley-VCH$d2009 215 $a1 online resource (450 p.) 225 0 $6880-03$aPhysics textbook 300 $aIncludes bibliographical references and index 311 $a3-527-40840-1 320 $aIncludes bibliographical references and index. 327 $aPhysics of Stochastic Processes; Contents; Preface; Part I Basic Mathematical Description; 1 Fundamental Concepts; 1.1 Wiener Process, Adapted Processes and Quadratic Variation; 1.2 The Space of Square Integrable Random Variables; 1.3 The Ito Integral and the Ito Formula; 1.4 The Kolmogorov Differential Equation and the Fokker-Planck Equation; 1.5 Special Diffusion Processes; 1.6 Exercises; 2 Multidimensional Approach; 2.1 Bounded Multidimensional Region; 2.2 From Chapman-Kolmogorov Equation to Fokker-Planck Description; 2.2.1 The Backward Fokker-Planck Equation; 2.2.2 Boundary Singularities 327 $a2.2.3 The Forward Fokker-Planck Equation2.2.4 Boundary Relations; 2.3 Different Types of Boundaries; 2.4 Equivalent Lattice Representation of Random Walks Near the Boundary; 2.4.1 Diffusion Tensor Representations; 2.4.2 Equivalent Lattice Random Walks; 2.4.3 Properties of the Boundary Layer; 2.5 Expression for Boundary Singularities; 2.6 Derivation of Singular Boundary Scaling Properties; 2.6.1 Moments of the Walker Distribution and the Generating Function; 2.6.2 Master Equation for Lattice Random Walks and its General Solution; 2.6.3 Limit of Multiple-Step Random Walks on Small Time Scales 327 $a2.6.4 Continuum Limit and a Boundary Model2.7 Boundary Condition for the Backward Fokker-Planck Equation; 2.8 Boundary Condition for the Forward Fokker-Planck Equation; 2.9 Concluding Remarks; 2.10 Exercises; Part II Physics of Stochastic Processes; 3 The Master Equation; 3.1 Markovian Stochastic Processes; 3.2 The Master Equation; 3.3 One-Step Processes in Finite Systems; 3.4 The First-Passage Time Problem; 3.5 The Poisson Process in Closed and Open Systems; 3.6 The Two-Level System; 3.7 The Three-Level System; 3.8 Exercises; 4 The Fokker-Planck Equation; 4.1 General Fokker-Planck Equations 327 $a4.2 Bounded Drift-Diffusion in One Dimension4.3 The Escape Problem and its Solution; 4.4 Derivation of the Fokker-Planck Equation; 4.5 Fokker-Planck Dynamics in Finite State Space; 4.6 Fokker-Planck Dynamics with Coordinate-Dependent Diffusion Coefficient; 4.7 Alternative Method of Solving the Fokker-Planck Equation; 4.8 Exercises; 5 The Langevin Equation; 5.1 A System of Many Brownian Particles; 5.2 A Traditional View of the Langevin Equation; 5.3 Additive White Noise; 5.4 Spectral Analysis; 5.5 Brownian Motion in Three-Dimensional Velocity Space; 5.6 Stochastic Differential Equations 327 $a5.7 The Standard Wiener Process5.8 Arithmetic Brownian Motion; 5.9 Geometric Brownian Motion; 5.10 Exercises; Part III Applications; 6 One-Dimensional Diffusion; 6.1 Random Walk on a Line and Diffusion: Main Results; 6.2 A Drunken Sailor as Random Walker; 6.3 Diffusion with Natural Boundaries; 6.4 Diffusion in a Finite Interval with Mixed Boundaries; 6.5 The Mirror Method and Time Lag; 6.6 Maximum Value Distribution; 6.7 Summary of Results for Diffusion in a Finite Interval; 6.7.1 Reflected Diffusion; 6.7.2 Diffusion in a Semi-Open System; 6.7.3 Diffusion in an Open System; 6.8 Exercises 327 $a7 Bounded Drift-Diffusion Motion 330 $aBased on lectures given by one of the authors with many years of experience in teaching stochastic processes, this textbook is unique in combining basic mathematical and physical theory with numerous simple and sophisticated examples as well as detailed calculations.In addition, applications from different fields are included so as to strengthen the background learned in the first part of the book. With its exercises at the end of each chapter (and solutions only available to lecturers) this book will benefit students and researchers at different educational levels.Solutions manual 410 0$aNew York Academy of Sciences 606 $aRandom measures$vProblems, exercises, etc 606 $aRandom measures 606 $aStatistical physics$vProblems, exercises, etc 606 $aStatistical physics 606 $aStochastic processes$vProblems, exercises, etc 606 $aStochastic processes 615 0$aRandom measures 615 0$aRandom measures. 615 0$aStatistical physics 615 0$aStatistical physics. 615 0$aStochastic processes 615 0$aStochastic processes. 676 $a519.23 686 $a417.1$2njb/09 686 $a519.23$2njb/09 700 $aMahnke$b R$g(Reinhard)$01382393 701 $aKaupuzs$b Jevgenijs$0941779 701 $aLubashevskii$b I. A$g(Igor' Alekseevich)$0941780 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139764203321 996 $aPhysics of stochastic processes$93425762 997 $aUNINA