Titlebook: Discrete Stochastic Processes and Applications; Jean-François Collet Textbook 2018 Springer International Publishing AG, part of Springer

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Science and Surgery: Bones in the Laboratory case of the Poisson process) rely on dicretizing the process, which means using skeletons. In order to keep the presentation elementary, some of the results we give are not optimal, and whenever necessary, references are given for sharper results.

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The Poisson process. will provide a gentle introduction to this method, which will be used again in the next chapter (with unfortunately many technical complications in the general case, where increments are not assumed to be stationary).

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Textbook 2018 probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy..

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Linear algebra and search enginesis why in order to make the presentation self-contained, most classical results on the Perron–Frobenius theory are included. The last section deals with the by now classical PageRank algorithm, which is included here because it is traditional to present it in the language of linear algebra rather than that of Markov processes.

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The Science of Surgery: Clinical Researchapproach for respectively random walks and birth–death models. For more examples of processes in scientific modeling we recommend the monograph [11], and for the particular case of random walks the interested reader should consult [19].

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