Random processes in physics and finance [[electronic resource] /] / Melvin Lax, Wei Cai, Min Xu

• Record Nr.: UNINA9910465815103321
• Autore: Lax Melvin J
• Pubbl/distr/stampa: Oxford ; ; New York, : Oxford University Press, 2006
• ISBN: 0-19-967380-2; 1-280-84565-1; 0-19-151378-4; 1-4294-5932-8
• Descrizione fisica: 1 online resource (342 p.)
• Collana: Oxford finance
• Altri autori (Persone): CaiWei; XuMin
• Disciplina: 530.15828
• Soggetti: Stochastic processes; Finance - Statistical methods; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. [307]-321) and index.
• Nota di contenuto: Contents; 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; 2.1 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; 4.1 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 ω 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; 6.3 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; 8.3 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; 9.3 Homogeneous noise with linear damping
• Sommario/riassunto: Melvin 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