LEADER 05577nam 2200721Ia 450 001 9910465815103321 005 20200520144314.0 010 $a0-19-967380-2 010 $a1-280-84565-1 010 $a0-19-151378-4 010 $a1-4294-5932-8 035 $a(CKB)2560000000298312 035 $a(EBL)430381 035 $a(OCoLC)609829766 035 $a(SSID)ssj0000232538 035 $a(PQKBManifestationID)11206460 035 $a(PQKBTitleCode)TC0000232538 035 $a(PQKBWorkID)10214633 035 $a(PQKB)10333498 035 $a(StDuBDS)EDZ0000072340 035 $a(MiAaPQ)EBC430381 035 $a(Au-PeEL)EBL430381 035 $a(CaPaEBR)ebr10271390 035 $a(CaONFJC)MIL84565 035 $a(EXLCZ)992560000000298312 100 $a20060403d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRandom processes in physics and finance$b[electronic resource] /$fMelvin Lax, Wei Cai, Min Xu 210 $aOxford ;$aNew York $cOxford University Press$d2006 215 $a1 online resource (342 p.) 225 1 $aOxford finance 300 $aDescription based upon print version of record. 311 $a0-19-856776-6 311 $a0-19-171835-1 320 $aIncludes bibliographical references (p. [307]-321) and index. 327 $aContents; A Note from Co-authors; 1 Review of probability; 1.1 Meaning of probability; 1.2 Distribution functions; 1.3 Stochastic variables; 1.4 Expectation values for single random variables; 1.5 Characteristic functions and generating functions; 1.6 Measures of dispersion; 1.7 Joint events; 1.8 Conditional probabilities and Bayes' theorem; 1.9 Sums of random variables; 1.10 Fitting of experimental observations; 1.11 Multivariate normal distributions; 1.12 The laws of gambling; 1.13 Appendix A: The Dirac delta function; 1.14 Appendix B: Solved problems; 2 What is a random process 327 $a2.1 Multitime probability description2.2 Conditional probabilities; 2.3 Stationary, Gaussian and Markovian processes; 2.4 The Chapman-Kolmogorov condition; 3 Examples of Markovian processes; 3.1 The Poisson process; 3.2 The one dimensional random walk; 3.3 Gambler's ruin; 3.4 Diffusion processes and the Einstein relation; 3.5 Brownian motion; 3.6 Langevin theory of velocities in Brownian motion; 3.7 Langevin theory of positions in Brownian motion; 3.8 Chaos; 3.9 Appendix A: Roots for the gambler's ruin problem; 3.10 Appendix B: Gaussian random variables; 4 Spectral measurement and correlation 327 $a4.1 Introduction: An approach to the spectrum of a stochastic process4.2 The definitions of the noise spectrum; 4.3 The Wiener-Khinchine theorem; 4.4 Noise measurements; 4.5 Evenness in ? of the noise?; 4.6 Noise for nonstationary random variables; 4.7 Appendix A: Complex variable notation; 5 Thermal noise; 5.1 Johnson noise; 5.2 Equipartition; 5.3 Thermodynamic derivation of Johnson noise; 5.4 Nyquist's theorem; 5.5 Nyquist noise and the Einstein relation; 5.6 Frequency dependent diffusion constant; 6 Shot noise; 6.1 Definition of shot noise; 6.2 Campbell's two theorems 327 $a6.3 The spectrum of filtered shot noise6.4 Transit time effects; 6.5 Electromagnetic theory of shot noise; 6.6 Space charge limiting diode; 6.7 Rice's generalization of Campbell's theorems; 7 The fluctuation-dissipation theorem; 7.1 Summary of ideas and results; 7.2 Density operator equations; 7.3 The response function; 7.4 Equilibrium theorems; 7.5 Hermiticity and time reversal; 7.6 Application to a harmonic oscillator; 7.7 A reservoir of harmonic oscillators; 8 Generalized Fokker-Planck equation; 8.1 Objectives; 8.2 Drift vectors and diffusion coefficients 327 $a8.3 Average motion of a general random variable8.4 The generalized Fokker-Planck equation; 8.5 Generation-recombination (birth and death) process; 8.6 The characteristic function; 8.7 Path integral average; 8.8 Linear damping and homogeneous noise; 8.9 The backward equation; 8.10 Extension to many variables; 8.11 Time reversal in the linear case; 8.12 Doob's theorem; 8.13 A historical note and summary (M. Lax); 8.14 Appendix A: A method of solution of first order PDEs; 9 Langevin processes; 9.1 Simplicity of Langevin methods; 9.2 Proof of delta correlation for Markovian processes 327 $a9.3 Homogeneous noise with linear damping 330 $aMelvin Lax was a member of the US National Academy of Sciences, and widely known for his contributions in the field of random processes in physics. This book uniquely presents Lax's theoretical treatment of random processes, including applications to laser and semiconductor physics, light propagation in scattering media, and investment decisions. - ;This respected high-level text is aimed at students and professionals working on random processes in various areas, including physics and finance. The first author, Melvin Lax (1922-2002) was a distinguished Professor of Physics at City College of 410 0$aOxford finance. 606 $aStochastic processes 606 $aFinance$xStatistical methods 608 $aElectronic books. 615 0$aStochastic processes. 615 0$aFinance$xStatistical methods. 676 $a530.15828 700 $aLax$b Melvin J$048516 701 $aCai$b Wei$021811 701 $aXu$b Min$0879309 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465815103321 996 $aRandom processes in physics and finance$92172252 997 $aUNINA