- 物理学家用的随机过程(英文版)
- - 作者：(美)K.雅各布斯
  - 出版社：世界图书出版公司
  - ISBN：9787519244668
  - 出版日期：2018/05/01
  - 页数：188
- 售价：19.2

内容大纲
随机过程广泛存在于物理学、生物学、化学和金融等领域。K.雅各布斯著的《物理学家用的随机过程(英文版)》是一部教材，书中提供了应用于物理学的随机过程和随机计算的基本理论，特点是不需要测度论知识就可学习本书内容。为了便于读者理解和掌握所学知识，全书共有70余例习题。目次：概率论综述；微分方程；高斯噪声随机方程；随机过程的特性；高斯噪声的应用；高斯噪声用的数值方法；Fokker-Planck方程和反应扩散系统；跳跃过程；levy过程；现代概率论。附录：高斯积分计算。读者对象：物理学及相关专业的研究生和科研人员。
作者介绍
目录
Preface
Acknowledgments
1  A review of probability theory
  1.1  Random variables and mutually exclusive events
  1.2  Independence
  1.3  Dependent random variables
  1.4  Correlations and correlation coefficients
  1.5  Adding independent random variables together
  1.6  Transformations of a random variable
  1.7  The distribution function
  1.8  The characteristic function
  1.9  Moments and cumulants
  1.10  The multivariate Gaussian
2  Differential equations
  2.1  Introduction
  2.2  Vector differential equations
  2.3  Writing differential equations using differentials
  2.4  Two methods for solving differential equations
    2.4.1  A linear differential equation with driving
  2.5  Solving vector linear differential equations
  2.6  Diagonalizing a matrix
3  Stochastic equations with Gaussian noise
  3.1  Introduction
  3.2  Gaussian increments and the continuum limit
  3.3  Interlude: why Gaussian noise?
  3.4  Ito calculus
  3.5  Ito's formula: changing variables in an SDE
  3.6  Solving some stochastic equations
    3.6.1  The Ornstein-Uhlenbeck process
    3.6.2  The full linear stochastic equation
    3.6.3  Ito stochastic integrals
  3.7  Deriving equations for the means and variances
  3.8  Multiple variables and multiple noise sources
    3.8.1  Stochastic equations with multiple noise sources
    3.8.2  Ito's formula for multiple variables
    3.8.3  Multiple Ito stochastic integrals
    3.8.4  The multivariate linear equation with additive noise
    3.8.5  The full multivariate linear stochastic equation
  3.9  Non-anticipating functions
4  Further properties of stochastic processes
  4.1  Sample paths
  4.2  The reflection principle and the first-passage time
  4.3  The stationary auto-correlation function, g
  4.4  Conditional probability densities
  4.5  The power spectrum
    4.5.1  Signals with finite energy
    4.5.2  Signals with finite power
  4.6  White noise
5  Some applications of Gaussian noise
  5.1  Physics: Brownian motion

  5.2  Finance: option pricing
    5.2.1  Some preliminary concepts
    5.2.2  Deriving the Black-Scholes equation
    5.2.3  Creating a portfolio that is equivalent to an option
    5.2.4  The price of a "European" option
  5.3  Modeling multiplicative noise in real systems: Stratonovich integrals
6  Numerical methods for Gaussian noise
  6.1  Euler's method
    6.1.1  Generating Gaussian random variables
  6.2  Checking the accuracy of a solution
  6.3  The accuracy of a numerical method
  6.4  Milstein's method
    6.4.1  Vector equations with scalar noise
    6.4.2  Vector equations with commutative noise
    6.4.3  General vector equations
  6.5  Runge-Kutta-like methods
  6.6  Implicit methods
  6.7  Weak solutions
    6.7.1  Second-order weak methods
7  Fokker-Planck equations and reaction--diffusion systems
  7.1  Deriving the Fokker-Planck equation
  7.2  The probability current
  7.3  Absorbing and reflecting boundaries
  7.4  Stationary solutions for one dimension
  7.5  Physics: thermalization of a single particle
  7.6  Time-dependent solutions
    7.6.1  Green's functions
  7.7  Calculating first-passage times
    7.7.1  The time to exit an interval
    7.7.2  The time to exit through one end of an interval
  7.8  Chemistry: reaction-diffusion equations
  7.9  Chemistry: pattern formation in reaction-diffusion systems
8  Jump processes
  8.1  The Poisson process
  8.2  Stochastic equations for jump processes
  8.3  The master equation
  8.4  Moments and the generating function
  8.5  Another simple jump process: "telegraph noise"
  8.6  Solving the master equation: a more complex example
  8.7  The general form of the master equation
  8.8  Biology: predator-prey systems
  8.9  Biology: neurons and stochastic resonance
9  Levy processes
  9.1  Introduction
  9.2  The stable Levy processes
    9.2.1  Stochastic equations with the stable processes
    9.2.2  Numerical simulation
  9.3  Characterizing all the Levy processes
  9.4  Stochastic calculus for Levy processes
    9.4.1  The linear stochastic equation with a Levy process

10 Modern probability theory
  10.1  Introduction
  10.2  The set of all samples
  10.3  The collection of all events
  10.4  The collection of events forms a sigma-algebra
  10.5  The probability measure
  10.6  Collecting the concepts: random variables
  10.7  Stochastic processes: filtrations and adapted processes
    10.7.1  Martingales
  10.8  Translating the modem language
Appendix A Calculating Gaussian integrals
References
Index

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