An Introduction to Stochastic ModelingServing as the foundation for a onesemester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Third Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems.

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Excellent textbook. Markov Chains are extensively treated,
analysis are specially placed and real problems emerge frequently.
But, there is also a lack of sensibility with difficult of problems,
where the problems section arise there's no indicator of how much
difficult it is.
Contents
Conditional Probability and Conditional  57 
Introduction  95 
The Long Run Behavior of Markov Chains  199 
Poisson Processes  267 
Continuous Time Markov Chains  333 
Processes  366 
Renewal Phenomena  419 
The Asymptotic Behavior of Renewal Processes  437 
Brownian Motion with Drift  508 
The OrnsteinUhlenbeck Process  524 
Queueing Systems  541 
Poisson Arrivals Exponential Service Times  547 
General Service Time Distributions  558 
Variations and Extensions  567 
Open Acyclic Queueing Networks  581 
General Open Networks  592 
Generalizations and Variations on Renewal Processes  447 
Discrete Renewal Theory  457 
Brownian Motion and Related Processes  473 
The Maximum Variable and the Reflection Principle  491 
Variations and Extensions  498 
601  
Answers to Exercises  603 
625  
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An Introduction to Stochastic Modeling Howard M. Taylor,Howard E. Taylor,Samuel Karlin Snippet view  1984 
Common terms and phrases
according analysis arrival assume average balls begins birth and death Brownian motion calculations called component conditional Consider constant continuous corresponding cost customers death process defined denote density function derive Determine distribution function distribution with parameter duration equally equation evaluate event example Exercises expected exponentially distributed failure Figure fixed formula fraction given gives identically independent individual initial integers interval length limiting limiting distribution long run Markov chain mean observed obtain occurs offspring operating particles period Poisson distribution Poisson process population positive possible Pr{X Problems process of rate queue random variables renewal process replacement respectively result sample server Show single solution standard starting stationary step stochastic successive Suppose Theorem tion transition probability matrix unit variance verify waiting zero