• Jean-François Collet
Part of the Universitext book series (UTX)


We shall now take a much more applied point of view, and present some illustrative examples for the general theory of the previous chapters. The emphasis will be on computations rather than mathematical issues such as summability and differentiability. As is often the case in modeling, discrete-time processes will be defined by specifying a one-step transition matrix, and continuous-time process by specifying a generator; we shall implement this approach 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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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire J.A. DieudonnéUniversité de Nice Sophia-AntipolisNice Cedex 02France

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