随机过程广泛存在于物理学、生物学、化学和金融等领域。本书是一部教材，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。

   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

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K.雅各布斯（Kurt Jacobs）是美国马萨诸塞州立大学教授，2014年，出版了另一部著作Quantum Measurement Theory and its Applications。