Random processes in physics and finance / / Melvin Lax, Wei Cai, Min Xu

• Record Nr.: UNINA9910968477703321
• Autore: Lax Melvin J
• Pubbl/distr/stampa: Oxford ; ; New York, : Oxford University Press, 2006
• ISBN: 9780191513787; 0191513784; 9780191718359; 0191718351; 9781429459327; 1429459328; 9780199673803; 0199673802; 9781280845659; 1280845651
• Edizione: [1st ed.]
• Descrizione fisica: xiii, 327 p. : ill
• Collana: Oxford finance
• Altri autori (Persone): CaiWei; XuMin
• Disciplina: 530.15828
• Soggetti: Stochastic processes; Finance - Statistical methods
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references (p. [307]-321) and index.
• Nota di contenuto: Intro -- 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 description -- 2.2 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 process -- 4.2 The definitions of the noise spectrum -- 4.3 The Wiener-Khinchine theorem -- 4.4 Noise measurements -- 4.5 Evenness in &amp -- #969 -- 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 noise -- 6.4 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 variable -- 8.4 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 -- 9.4 Conditional correlations -- 9.5 Generalized characteristic functions -- 9.6 Generalized shot noise -- 9.7 Systems possessing inertia -- 10 Langevin treatment of the Fokker-Planck process -- 10.1 Drift velocity -- 10.2 An example with an exact solution -- 10.3 Langevin equation for a general random variable -- 10.4 Comparison with Ito's calculus lemma -- 10.5 Extending to the multiple dimensional case -- 10.6 Means of products of random variables and noise source -- 11 The rotating wave van del Pol oscillator (RWVP) -- 11.1 Why is the laser line-width so narrow?.; 11.2 An oscillator with purely resistive nonlinearities -- 11.3 The diffusion coefficient -- 11.4 The van der Pol oscillator scaled to canonical form -- 11.5 Phase fluctuations in a resistive oscillator -- 11.6 Amplitude fluctuations -- 11.7 Fokker-Planck equation for RWVP -- 11.8 Eigenfunctions of the Fokker-Planck operator -- 12 Noise in homogeneous semiconductors -- 12.1 Density of states and statistics of free carriers -- 12.2 Conductivity fluctuations -- 12.3 Thermodynamic treatment of carrier fluctuations -- 12.4 General theory of concentration fluctuations -- 12.5 Influence of drift and diffusion on modulation noise -- 13 Random walk of light in turbid media -- 13.1 Introduction -- 13.2 Microscopic statistics in the direction space -- 13.3 The generalized Poisson distribution p[sub(n)](t) -- 13.4 Macroscopic statistics -- 14 Analytical solution of the elastic ; transport equation -- 14.1 Introduction -- 14.2 Derivation of cumulants to an arbitrarily high order -- 14.3 Gaussian approximation of the distribution function -- 14.4 Improving cumulant solution of the transport equation -- 15 Signal extraction in presence of smoothing and noise -- 15.1 How to deal with ill-posed problems -- 15.2 Solution concepts -- 15.3 Methods of solution -- 15.4 Well-posed stochastic extensions of ill-posed processes -- 15.5 Shaw's improvement of Franklin's algorithm -- 15.6 Statistical regularization -- 15.7 Image restoration -- 16 Stochastic methods in investment decision -- 16.1 Forward contracts -- 16.2 Futures contracts -- 16.3 A variety of futures -- 16.4 A model for stock prices -- 16.5 The Ito's stochastic differential equation -- 16.6 Value of a forward contract on a stock -- 16.7 Black-Scholes differential equation -- 16.8 Discussion -- 16.9 Summary -- 17 Spectral analysis of economic time series -- 17.1 Overview.; 17.2 The Wiener-Khinchine and Wold theorems -- 17.3 Means, correlations and the Karhunen-Loeve theorem -- 17.4 Slepian functions -- 17.5 The discrete prolate spheroidal sequence -- 17.6 Overview of Thomson's procedure -- 17.7 High resolution results -- 17.8 Adaptive weighting -- 17.9 Trend removal and seasonal adjustment -- 17.10 Appendix A: The sampling theorem -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.
• Sommario/riassunto: This book uniquely presents the theoretical treatment of random processes in physics and finance, including applications to laser and semiconductor physics, light propagation in scattering media and investment decisions.