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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.

    (a)X(2t)

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

    upload_2015-6-17_0-58-42.png

    and similarly

    Given Poisson process X(t)

    (a) X(2t)

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

    upload_2015-6-17_1-1-21.png

    BUT

    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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    Science Advisor
    Homework Helper

    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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