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物理學家用的隨機過程(英文版)

  • 作者:(美)K.雅各布斯
  • 出版社:世界圖書出版公司
  • ISBN:9787519244668
  • 出版日期:2018/05/01
  • 裝幀:平裝
  • 頁數:188
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內容大鋼
    隨機過程廣泛存在於物理學、生物學、化學和金融等領域。K.雅各布斯著的《物理學家用的隨機過程(英文版)》是一部教材,書中提供了應用於物理學的隨機過程和隨機計算的基本理論,特點是不需要測度論知識就可學習本書內容。為了便於讀者理解和掌握所學知識,全書共有70余例習題。目次:概率論綜述;微分方程;高斯雜訊隨機方程;隨機過程的特性;高斯雜訊的應用;高斯雜訊用的數值方法;Fokker-Planck方程和反應擴散系統;跳躍過程;levy過程;現代概率論。附錄:高斯積分計算。讀者對象:物理學及相關專業的研究生和科研人員。

作者介紹
(美)K.雅各布斯

目錄
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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