概率论教程

出版时间：2012-5  出版社：世界图书出版公司  作者：Achim Klenke  页数：616  
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内容概要

　　《概率论教程》是一部讲述现代概率论及其测度论应用基础的教程，其目标读者是该领域的研究生和相关的科研人员。内容广泛，有许多初级教程不能涉及到得的。理论叙述严谨，独立性强。有关测度的部分和概率的章节相互交织，将概率的抽象性完全呈现出来。此外，还有大量的图片、计算模拟、重要数学家的个人传记和大量的例子。这使得表现形式更加活跃。

作者简介

作者:(德)凯兰克

书籍目录

preface 1 basic measure theory 1.1 classes of sets 1.2 set functions 1.3 the measure extension theorem 1.4 measurable maps 1.5 random variables 2 independence 2.1 independence of events 2.2 independent random variables 2.3 kolmogorov's 0-1 law 2.4 example: percolation 3 generating functions 3.1 definition and examples 3.2 poisson approximation 3.3 branching processes 4 the integral 4.1 construction and simple properties 4.2 monotone convergence and fatou's lemma .4.3 lebesgue integral versus riemann integral 5 moments and laws of large numbers 5.1 moments 5.2 weak law of large numbers 5.3 strong law of large numbers 5.4 speed of convergence in the strong lln 5.5 the poisson process 6 convergence theorems 6.1 almost sure and measure convergence 6.2 uniform integrability 6.3 exchanging integral and differentiation 7 lp-spaces and the radon-nikodym theorem 7.1 definitions 7.2 inequalities and the fischer-riesz theorem 7.3 hilbert spaces 7.4 lebesgue's decomposition theorem 7.5 supplement: signed measures 7.6 supplement: dual spaces 8 conditional expectations 8.1 elementary conditional probabilities 8.2 conditional expectations 8.3 regular conditional distribution 9 martingales 9.1 processes, filtrations, stopping times 9.2 martingales 9.3 discrete stochastic integral 9.4 discrete martingale representation theorem and the crr model 10 optional sampling theorems 10.1 doob decomposition and square variation 10.2 optional sampling and optional stopping 10.3 uniform integrability and optional sampling 11 martingale convergence theorems and their applications 11.1 doob's inequality 11.2 martingale convergence theorems 11.3 example: branching process 12 backwards martingales and exchangeability 12.1 exchangeable families of random variables 12.2 backwards martingales 12.3 de finetti's theorem 13 convergence of measures 13.1 a topology primer 13.2 weak and vague convergence 13.3 prohorov's theorem 13.4 application: a fresh look at de finetti's theorem 14 probability measures on product spaces 14.1 product spaces 14.2 finite products and transition kernels 14.3 kolmogorov's extension theorem 14.4 markov semigroups 15 characteristic functions and the central limit theorem 15.1 separating classes of functions 15.2 characteristic functions: examples 15.3 l6vy's continuity theorem 15.4 characteristic functions and moments 15.5 the central limit theorem 15.6 multidimensional central limit theorem 16 infinitely divisible distributions 16.1 l6vy-khinchin formula 16.2 stable distributions 17 markov chains 17.1 definitions and construction 17.2 discrete markov chains: examples 17.3 discrete markov processes in continuous time 17.4 discrete markov chains: recurrence and transience 17.5 application: recurrence and transience of random walks 17.6 invariant distributions 18 convergence of markov chains 18.1 periodicity of markov chains 18.2 coupling and convergence theorem 18.3 markov chain monte carlo method 18.4 speed of convergence 19 markov chains and electrical networks 19.1 harmonic functions 19.2 reversible markov chains 19.3 finite electrical networks 19.4 recurrence and transience 19.5 network reduction 19.6 random walk in a random environment 20 ergodic theory 20.1 definitions 20.2 ergodic theorems 20.3 examples 20.4 application: recurrence of random walks 20.5 mixing 21 brownian motion 21.1 continuous versions 21.2 construction and path properties 21.3 strong markov property 21.4 supplement: feller processes 21.5 construction via l2-approximation 21.6 the space c([0, ∞)) 21.7 convergence of probability measures on c([0, ∞)) 21.8 donsker's theorem 21.9 pathwise convergence of branching processes 21.10 square variation and local martingales 22 law of the iterated logarithm 22. l iterated logarithm for the brownian motion 22.2 skorohod's embedding theorem 22.3 hartman-wintner theorem 23 large deviations 23.1 cramer's theorem 23.2 large deviations principle 23.3 sanov's theorem 23.4 varadhan's lemma and free energy 24 the poisson point process 24.1 random measures 24.2 properties of the poisson point process 24.3 the poisson-dirichlet distribution 25 the it6 integral 25.1 it6 integral with respect to brownian motion 25.2 it6 integral with respect to diffusions 25.3 the it6 formula 25.4 dirichlet problem and brownian motion 25.5 recurrence and transience of brownian motion 26 stochastic differential equations 26.1 strong solutions 26.2 weak solutions and the martingale problem 26.3 weak uniqueness via duality references notation index name index subject index

编辑推荐

《概率论教程 》是一部讲述现代概率论及其测度论应用基础的教程，其目标读者是该领域的研究生和相关的科研人员。内容广泛，有许多初级教程不能涉及到得的。理论叙述严谨，独立性强。有关测度的部分和概率的章节相互交织，将概率的抽象性完全呈现出来。此外，还有大量的图片、计算模拟、重要数学家的个人传记和大量的例子。这使得表现形式更加活跃。本书由凯兰克著。

用户评论 (总计2条)

•   这本书内容，印刷均属上层，是不可多得的研究生教材~
•   该书是概率内容方面比较齐全的一本好书。