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  • 概率论教程[平装]
  • 共3个商家     59.30元~71.89
  • 作者:凯兰克(作者)
  • 出版社:世界图书出版公司;第1版(2012年6月1日)
  • 出版时间:
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  • ISBN:9787510044113

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    《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。

    作者简介

    作者:(德)凯兰克

    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