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This course will introduce some concepts and methods in applied probability and stochastic modelling, with an emphasis on business applications. Topics covered include probability basics; discrete-time Markov chains and processes; exponential distribution and the Poisson process; continuous-time Markov chains; introduction to Brownian motion.
本课程将介绍应用概率和随机建模的一些概念和方法，重点是商业应用。涉及的主题包括概率基础知识；离散时间马尔可夫链和过程；指数分布和泊松过程；连续时间马尔可夫链；布朗运动介绍。
The book provides a pedagogical examination of the way in which stochastic models are encountered in applied sciences and techniques such as physics, engineering, biology and genetics, economics and social sciences. It covers Markov and semi-Markov models, as well as their particular cases: Poisson, renewal processes, branching processes, Ehrenfest models, genetic models, optimal stopping, reliability, reservoir theory, storage models, and queuing systems.
The book features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus. KEY TOPICS: Combinatorial Analysis; Axioms of Probability; Conditional Probability and Independence; Random Variables; Continuous Random Variables; Jointly Distributed Random Variables; Properties of Expectation; Limit Theorems; Additional Topics in Probability; Simulation MARKET: For all readers interested in probability.
This book contains material on compound Poisson random variables including an identity which can be used to efficiently compute moments, Poisson approximations, and coverage of the mean time spent in transient states as well as examples relating to the Gibb's sampler, the Metropolis algorithm and mean cover time in star graphs.
