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If X(t) is gaussian process, How about X(2t)?

  1. Jun 14, 2015 #1
    written as title,

    1.
    If X(t) is gaussian process, then

    Can I say that X(2t) is gaussian process?

    of course, 2*X(t) is gaussian process

    2. If X(t) is poisson process, then

    X(2t) is also poisson process?
     
    Last edited: Jun 14, 2015
  2. jcsd
  3. Jun 14, 2015 #2

    mathman

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    In both cases you have a stochastic process where the element at a particular value of t has the specified distribution. Changing the scale factor doesn't affect that property.
     
  4. Jun 14, 2015 #3
    THANKS
     
  5. Jul 1, 2015 #4
    Of course when ##X(t)## is gauss process, ##X(2t)## is also gauss cuz ##X(2t)=2X(t)## applied by ##f(\alpha x)=\alpha f(x)## .
     
  6. Jul 1, 2015 #5

    Mark44

    Staff: Mentor

    I don't know anything about Gaussian processes, but I doubt very much that X(2t) = 2X(t). For most functions, ##f(\alpha x) \neq \alpha f(x)##.
     
  7. Jul 1, 2015 #6
    What do you mean?
     
  8. Jul 1, 2015 #7

    Mark44

    Staff: Mentor

    What I mean is that, in general, functions aren't linear. Here are a few examples:
    ##\cos(2x) \neq 2\cos(x)##
    ##\sqrt{2x} \neq 2\sqrt{x}##
    ##\ln(2x) \neq 2\ln(x)##
    ##10^{2x} \neq 2\cdot 10^x##
    etc.
     
  9. Jul 1, 2015 #8

    FactChecker

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    A Gaussian process, X(y), in variable y is just any process that is a normally distributed random variable for every value of y. It is not important the the variable y is time or not. If X(t) is a Gaussian process in time t, let y=2t, The process X(y) is a normally distributed random variable at y whose parameters, mean and variance are the same as X(t) where t=y/2 . So X(y), y=2t is also a Gaussian process. The Poisson process is similar, but not as simple. Since the Poison properties are very dependent on time t, changing to another variable y=2t is not so obvious. You should check if all the Poisson properties still apply with the new variable y.
     
  10. Jul 2, 2015 #9
    We are talking about Gauss process so the functions ##f## of it are linear
     
  11. Jul 2, 2015 #10

    Mark44

    Staff: Mentor

    Please provide a link to justify this claim.
     
  12. Jul 2, 2015 #11
    You just search on google, ok im done here. The end of reply
     
  13. Jul 2, 2015 #12

    Mark44

    Staff: Mentor

    You made the claim - it's up to you to justify it.
     
  14. Jul 2, 2015 #13

    FactChecker

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    That is not right. Saying a process is Gaussian doesn't say anything about the relationship between X(t) and X(2t).
     
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