## 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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a₁ arrival process B₁ B₂ Bernoulli process bounded function closed set Compute the limiting Consider Corollary corresponding defined definition denote discrete random variable eigenvalue eigenvector equal event expected number expected value exponential distribution finite fixed form a Poisson function ƒ given Hence identically distributed implies independent and identically infinite integral interarrival interval irreducible recurrent jumps Lemma lifetime limiting distribution Markov chain Markov process Markov renewal process N₁ non-negative number of arrivals number of visits obtain optimal stopping P₁ parameter periodic with period process with rate Proposition queue recurrent non-null recurrent null renewal equation renewal theory result right continuous S₁ sample space satisfies semi-Markov process semi-regenerative sequence solution stochastic process successive Suppose T₁ T₂ taking values tion transient transition function transition matrix W₁ X₁ X₂ Xn+1 Y₁