物理学家用的随机过程(影印版) 目录

PrefaceAcknowledgments1A review of probability theory1.1Random variables and mutually exclusive events1.2Independence1.3Dependent random variables1.4Correlations and correlation coefficients1.5Adding independent random variables together1.6Transformations of a random variable1.7The distribution function1.8The characteristic function1.9Moments and cumulants1.10The multivariate Gaussian2Differential equations2.1Introduction2.2Vector differential equations2.3Writing differential equations using differentials2.4Two methods for solving differential equations2.4.1A linear differential equation with driving2.5Solving vector linear differential equations2.6Diagonalizing a matrix3Stochastic equations with Gaussian noise3.1Introduction3.2Gaussian increments and the continuum limit3.3Interlude: why Gaussian noise?3.4Ito calculus3.5Ito's formula: changing variables in an SDE3.6Solving some stochastic equations3.6.1The Ornstein-Uhlenbeck process3.6.2The full linear stochastic equation3.6.3Ito stochastic integrals3.7Deriving equations for the means and variances3.8Multiple variables and multiple noise sources3.8.1Stochastic equations with multiple noise sources3.8.2Ito's formula for multiple variables3.8.3Multiple Ito stochastic integrals3.8.4The multivariate linear equation with additive noise3.8.5The full multivariate linear stochastic equation3.9Non-anticipating functions4Further properties of stochastic processes4.1Sample paths4.2The reflection principle and the first-passage time4.3The stationary auto-correlation function, g4.4Conditional probability densities4.5The power spectrum4.5.1Signals with finite energy4.5.2Signals with finite power4.6White noise5Some applications of Gaussian noise5.1Physics: Brownian motion5.2Finance: option pricing5.2.1Some preliminary concepts5.2.2Deriving the Black-Scholes equation5.2.3Creating a portfolio that is equivalent to an option5.2.4The price of a "European" option5.3Modeling multiplicative noise in real systems: Stratonovich integrals6Numerical methods for Gaussian noise6.1Euler's method6.1.1Generating Gaussian random variables6.2Checking the accuracy of a solution6.3The accuracy of a numerical method6.4Milstein's method6.4.1Vector equations with scalar noise6.4.2Vector equations with commutative noise6.4.3General vector equations6.5Runge-Kutta-like methods6.6Implicit methods6.7Weak solutions6.7.1Second-order weak methods7Fokker-Planck equations and reaction--diffusion systems7.1Deriving the Fokker-Planck equation7.2The probability current7.3Absorbing and reflecting boundaries7.4Stationary solutions for one dimension7.5Physics: thermalization of a single particle7.6Time-dependent solutions7.6.1Green's functions7.7Calculating first-passage times7.7.1The time to exit an interval7.7.2The time to exit through one end of an interval7.8Chemistry: reaction-diffusion equations7.9Chemistry: pattern formation in reaction-diffusion systems8Jump processes8.1The Poisson process8.2Stochastic equations for jump processes8.3The master equation8.4Moments and the generating function8.5Another simple jump process: "telegraph noise"8.6Solving the master equation: a more complex example8.7The general form of the master equation8.8Biology: predator-prey systems8.9Biology: neurons and stochastic resonance9Levy processes9.1Introduction9.2The stable Levy processes9.2.1Stochastic equations with the stable processes9.2.2Numerical simulation9.3Characterizing all the Levy processes9.4Stochastic calculus for Levy processes9.4.1The linear stochastic equation with a Levy process10 Modern probability theory10.1Introduction10.2The set of all samples10.3The collection of all events10.4The collection of events forms a sigma-algebra10.5The probability measure10.6Collecting the concepts: random variables10.7Stochastic processes: filtrations and adapted processes10.7.1Martingales10.8Translating the modem languageAppendix A Calculating Gaussian integralsReferencesIndex%

物理学家用的随机过程(影印版) 作者简介

《物理学家用的随机过程》作者Kurt Jacobs（美国，K. 雅各布斯），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。

物理学家用的随机过程(影印版) 内容简介

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。

物理学家用的随机过程(影印版) 作者简介

《物理学家用的随机过程》作者Kurt Jacobs（美国，K. 雅各布斯），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。