Stochastic Processes

  • Vincenzo Capasso
  • David Bakstein
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


We commence along the lines of the founding work of Kolmogorov by regarding stochastic processes as a family of random variables defined on a probability space and thereby define a probability law on the set of trajectories of the process. More specifically, stochastic processes generalize the notion of (finite-dimensional) vectors of random variables to the case of any family of random variables indexed in a general set T. Typically, the latter represents “time” and is an interval of \(\mathbb{R}\) (in the continuous case) or \(\mathbb{N}\) (in the discrete case). For a nice and elementary introduction to this topic, the reader may refer to Parzen (1962).


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Vincenzo Capasso
    • 1
  • David Bakstein
    • 1
  1. 1.ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences)Università degli Studi di MilanoMilanItaly

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