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Homework Help: About stochastic process...Help please

  1. Jun 16, 2015 #1
    Given a Gaussian process X(t), identify which of the following , if any, are gaussian processes.


    solution said that X(2t) is not gaussian process, since


    and similarly

    Given Poisson process X(t)

    (a) X(2t)

    soultion said that X(2t) is not poisson process, since same reason above.



    I think that in stochastic process, Time t is just constant value.

    so I think X(2t), X(10000t), X(t+100) is also gaussian process ,or poisson process

    doesn't care about whatever t is.

    answer is?
  2. jcsd
  3. Jun 16, 2015 #2

    Ray Vickson

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    You are correct; if one looks at the usual definition of a Gaussian process, Y(t) =X(2t) satisfies the definition. However, its ##\mu## and ##\sigma## are different from those of X(t). Maybe your book uses some really weird definition of Gaussian process, but I hope not---as that would be misleading generations of students. See, eg., https://en.wikipedia.org/wiki/Gaussian_process . The same remarks apply to your Poisson process case.

    Frankly, I am surprised someone would make those types of errors, because the scaling properties (of Poisson processes, in particular) are absolutely fundamental in modelling and applications.
  4. Jun 16, 2015 #3
    Thanks for reply vickson!
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