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

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1. Jun 14, 2015

### hojoon yang

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. Jun 14, 2015

### mathman

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.

3. Jun 14, 2015

THANKS

4. Jul 1, 2015

### Helolo

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. Jul 1, 2015

### Staff: Mentor

I don't know anything about Gaussian processes, but I doubt very much that X(2t) = 2X(t). For most functions, $f(\alpha x) \neq \alpha f(x)$.

6. Jul 1, 2015

### Helolo

What do you mean?

7. Jul 1, 2015

### 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.

8. Jul 1, 2015

### FactChecker

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.

9. Jul 2, 2015

### Helolo

We are talking about Gauss process so the functions $f$ of it are linear

10. Jul 2, 2015

### Staff: Mentor

11. Jul 2, 2015

### Helolo

You just search on google, ok im done here. The end of reply

12. Jul 2, 2015

### Staff: Mentor

You made the claim - it's up to you to justify it.

13. Jul 2, 2015

### FactChecker

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