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

  • #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:

Answers and Replies

  • #2
mathman
Science Advisor
7,968
507
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.
 
  • Like
Likes Helolo
  • #3
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.

THANKS
 
  • #4
7
0
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)## .
 
  • #5
35,224
7,042
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)## .
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)##.
 
  • #6
7
0
What do you mean?
 
  • #7
35,224
7,042
What do you mean?
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.
 
  • Like
Likes berkeman
  • #8
FactChecker
Science Advisor
Gold Member
6,531
2,607
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.
 
  • Like
Likes Helolo
  • #9
7
0
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.
We are talking about Gauss process so the functions ##f## of it are linear
 
  • #10
35,224
7,042
We are talking about Gauss process so the functions ##f## of it are linear
Please provide a link to justify this claim.
 
  • #11
7
0
Please provide a link to justify this claim.
You just search on google, ok im done here. The end of reply
 
  • #12
35,224
7,042
You just search on google, ok im done here. The end of reply
You made the claim - it's up to you to justify it.
 
  • Like
Likes PWiz
  • #13
FactChecker
Science Advisor
Gold Member
6,531
2,607
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)## .
That is not right. Saying a process is Gaussian doesn't say anything about the relationship between X(t) and X(2t).
 

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

Replies
4
Views
2K
  • Last Post
Replies
6
Views
823
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
16
Views
6K
Replies
13
Views
2K
  • Last Post
Replies
2
Views
888
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
7
Views
4K
  • Last Post
Replies
9
Views
2K
Top