Introduction to Stochastic ProcessesThis clear presentation of the most fundamental models of random phenomena employs methods that recognize computer-related aspects of theory. The text emphasizes the modern viewpoint, in which the primary concern is the behavior of sample paths. By employing matrix algebra and recursive methods, rather than transform methods, it provides techniques readily adaptable to computing with machines. Topics include probability spaces and random variables, expectations and independence, Bernoulli processes and sums of independent random variables, Poisson processes, Markov chains and processes, and renewal theory. Assuming some background in calculus but none in measure theory, the complete, detailed, and well-written treatment is suitable for engineering students in applied mathematics and operations research courses as well as those in a wide variety of other scientific fields. Many numerical examples, worked out in detail, appear throughout the text, in addition to numerous end-of-chapter exercises and answers to selected exercises. |
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applies arrivals becomes bounded called Chapter closed completes Compute conditional Consider constant continuous Conversely Corollary corresponding customers defined definition denote depends discrete distribution eigenvalue equal equation event EXAMPLE excessive Exercise exists expected value exponential fact failure Figure finite first fixed function f given gives hand Hence holds implies independent infinite initial integral interested interval jumps Lemma lifetime limit limiting distribution Markov chain Markov process mean measure non-negative observe obtain occurs optimal stopping otherwise parameter particular payoff period Poisson process positive possible preceding present probability problem Proof Proposition queue random variable reached recurrent remaining replaced respective result Riemann integrable satisfies sequence Show solution space starting successive Suppose taking term Theorem theory tion transient transition matrix units visits write yields