Probability Theory: A Comprehensive Course
Probability Theory: A Comprehensive Course
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DOI：
10.1007/978-1-84800-048-3
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发表时间：
2008-01
期刊：
影响因子：
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通讯作者：
A. Klenke
中科院分区：
文献类型：
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作者：
A. Klenke
这本受欢迎的教科书第二版包含了现代概率论的全面课程，涵盖了入门教科书中通常找不到的各种主题，包括：·随机变量和的极限定理·鞅·渗流·马尔可夫链和电网络·随机过程的构造·泊松点过程和无限可除性·大偏差原理和统计物理·布朗运动·随机积分和随机微分方程。该理论以一种严谨和完备的方式发展，测度论的章节与概率论的章节交错，以展示概率论中抽象概念的力量。这个第二版经过了仔细的扩展，包含了许多新功能。它包含了最新的数字(超过50个)、计算机模拟和一些困难的证据已经变得更容易获得。大量的例子和270多个练习以及关键数学家的传记细节支持和活跃了演讲。它将对物理学、计算机科学、经济学和生物学中的数学和统计学的学生和研究人员有所帮助。
This second edition of the popular textbook contains a comprehensive course in modern probability theory, covering a wide variety of topics which are not usually found in introductory textbooks, including:• limit theorems for sums of random variables• martingales• percolation• Markov chains and electrical networks• construction of stochastic processes• Poisson point process and infinite divisibility• large deviation principles and statistical physics• Brownian motion• stochastic integral and stochastic differential equations. The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology.