概率、马尔可夫链、队列和仿真:性能建模的数学基础 Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling

基本信息

Format：Hardback | 776 pages

Dimensions: 178 x 254 x 40.64mm | 1,474g

Publication date: 26 Jul 2009

Publisher：Princeton University Press

Imprint: Princeton University Press

ISBN: 9780691140629

页面参数仅供参考，具体以实物为准

内容简介

《概率、马尔科夫链、队列和模拟》对性能建模所依据的数学过程进行了现代和专业的处理。对数学推导的详细解释和大量的说明性例子使这本教科书很容易被学习随机过程发挥基本作用的课程的研究生和高级本科生所接受。该教科书与各种领域相关，包括计算机科学、工程、运筹学、统计学和数学。教材着眼于概率论的基础知识，从基于集合的概率的基本概念，到概率分布，再到边界、极限定理和大数定律。从理论和计算的角度分析了离散和连续时间马尔科夫链。主题包括Chapman-Kolmogorov方程；不可还原性；势、基本和可达性矩阵；随机行走问题；可逆性；更新过程；以及固定和瞬时分布的数值计算。

详细分析了M/M/1队列及其对更普遍的出生至死亡过程的扩展，以及具有阶段型到达和服务过程的队列。M/G/1和G/M/1队列使用嵌入式马尔科夫链进行求解；处理了繁忙期、剩余服务时间和优先调度、对开放和封闭的排队网络进行了分析。本书的末部讨论了模拟的数学基础，每一章都有大量的练习。还提供了一本教师的解决方案手册，其中所有的练习都是完整的，（仅对教授）。* 大量的例子阐明了数学理论 * 仔细详细的数学推导解释保证了有价值的教学方法 * 每章都有大量的练习题

This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives.

* Fully revised and expanded to reflect developments in the field since the financial crisis* Features shorter chapters to facilitate teaching and learning* Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing* Includes a new chapter on market risk and new material on risk measures and risk aggregation

作者简介

威廉·J·斯图尔特是北卡罗来纳州立大学的计算机科学教授。他是《马尔科夫链数值解法简介》（普林斯顿）的作者。

William J. Stewart is professor of computer science at North Carolina State University. He is the author of "An Introduction to the Numerical Solution of Markov Chains" (Princeton).

目录

Preface and Acknowledgments xv PART I PROBABILITY 1 Chapter 1: Probability 3 1.1 Trials, Sample Spaces, and Events 3 1.2 Probability Axioms and Probability Space 9 1.3 Conditional Probability 12 1.4 Independent Events 15 1.5 Law of Total Probability 18 1.6 Bayes' Rule 20 1.7 Exercises 21 Chapter 2: Combinatorics--The Art of Counting 25 2.1 Permutations 25 2.2 Permutations with Replacements 26 2.3 Permutations without Replacement 27 2.4 Combinations without Replacement 29 2.5 Combinations with Replacements 31 2.6 Bernoulli (Independent) Trials 33 2.7 Exercises 36 Chapter 3: Random Variables and Distribution Functions 40 3.1 Discrete and Continuous Rand...