Keywords:
Stochastic processes.
;
Finance -- Statistical methods.
;
Electronic books.
Description / Table of Contents:
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.
Type of Medium:
Online Resource
Pages:
1 online resource (342 pages)
Edition:
1st ed.
ISBN:
9780191513787
Series Statement:
Oxford Finance Series
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=430381
DDC:
530.15828
Language:
English
Note:
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 & -- #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.
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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?.
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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.
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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.
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