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Random processes in physics and finance [[electronic resource] /] / Melvin Lax, Wei Cai, Min Xu
| Random processes in physics and finance [[electronic resource] /] / Melvin Lax, Wei Cai, Min Xu |
| Autore | Lax Melvin J |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2006 |
| Descrizione fisica | 1 online resource (342 p.) |
| Disciplina | 530.15828 |
| Altri autori (Persone) |
CaiWei
XuMin |
| Collana | Oxford finance |
| Soggetto topico |
Stochastic processes
Finance - Statistical methods |
| Soggetto genere / forma | Electronic books. |
| ISBN |
0-19-967380-2
1-280-84565-1 0-19-151378-4 1-4294-5932-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910465815103321 |
Lax Melvin J
|
||
| Oxford ; ; New York, : Oxford University Press, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Random processes in physics and finance [[electronic resource] /] / Melvin Lax, Wei Cai, Min Xu
| Random processes in physics and finance [[electronic resource] /] / Melvin Lax, Wei Cai, Min Xu |
| Autore | Lax Melvin J |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2006 |
| Descrizione fisica | xiii, 327 p. : ill |
| Altri autori (Persone) |
CaiWei
XuMin |
| Collana | Oxford finance |
| Soggetto topico |
Stochastic processes
Finance - Statistical methods |
| ISBN |
0191513784
9780191513787 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910795752003321 |
|
Lax Melvin J
|
||
| Oxford ; ; New York, : Oxford University Press, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Random processes in physics and finance / / Melvin Lax, Wei Cai, Min Xu
| Random processes in physics and finance / / Melvin Lax, Wei Cai, Min Xu |
| Autore | Lax Melvin J |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Oxford ; ; New York, : Oxford University Press, 2006 |
| Descrizione fisica | xiii, 327 p. : ill |
| Disciplina | 530.15828 |
| Altri autori (Persone) |
CaiWei
XuMin |
| Collana | Oxford finance |
| Soggetto topico |
Stochastic processes
Finance - Statistical methods |
| ISBN |
9780191513787
0191513784 9780191718359 0191718351 9781429459327 1429459328 9780199673803 0199673802 9781280845659 1280845651 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 & -- #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. |
| Record Nr. | UNINA-9910968477703321 |
|
Lax Melvin J
|
||
| Oxford ; ; New York, : Oxford University Press, 2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||