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

Format:

Book

Author/Creator:

Lax, Melvin J.

Contributor:

Cai, Wei.

Xu, Min.

Series:

Oxford finance.

Oxford finance

Language:

English

Subjects (All):

Stochastic processes.

Finance--Statistical methods.

Finance.

Physical Description:

xiii, 327 p. : ill.

Edition:

1st ed.

Place of Publication:

Oxford ; New York : Oxford University Press, 2006.

Summary:

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.

Contents:

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.

Notes:

Includes bibliographical references (p. [307]-321) and index.

Description based on metadata supplied by the publisher and other sources.

Description based on publisher supplied metadata and other sources.

ISBN:

9780191513787

0191513784

9780191718359

0191718351

9781429459327

1429459328

9780199673803

0199673802

9781280845659

1280845651

OCLC:

609829766