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| karl... |
 Posted: Sat Oct 24, 2009 11:25 pm |
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Guest
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Henry schrieb:
[quote]On 24 Oct, 05:18, karl <oud... at (no spam) nononet.com> wrote:
Henry schrieb:
On 23 Oct, 19:16, karl <oud... at (no spam) nononet.com> wrote:
HJ said definitely white noise.
HJ's second post in the thread suggested an approximation, and
that is what I replied to
So you have shown that a wrong approximation gives a wrong
result.
That is your assertion, not mine. And you need to back it up with
something more substantial than your current comments.
[/quote]
Apparently you can't show that the integral over your approximations
converges to the integral over white noise. If I say that it does not
converge to the integral over white noise, you suddenly say that you
never claimed that.
It is easy to see that the autocovariance function of your
approximations is always less equal 1. But if these would converge to
white noise, the autocovariance function at zero had to go to
infinity, since the autocovariance of white noise is the Dirac delta
function. So no convergence to white noise.
[quote]
If you are going to say that white noise with a fixed finite
variance integrates to Brownian noise, I would interested to see
what you think the variance of the integral is.
[/quote]
Please explain the term "white noise with a fixed finite variance".
I guess you produce now your own definition of white noise.
The standard definition is that it is a generalized stationary
continuous-time stochastic process with mean zero whose spectral
density is constant (not zero) and
whose autocovariance function is a Dirac delta function. This you can
find in all textbooks.
There is no sense in discussing further if you now start using a private
definition of white noise different from the usual one given above.
Ciao
Karl |
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| Henry... |
| Posted: Sun Oct 25, 2009 9:01 pm |
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Guest
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On 25 Oct, 05:25, karl <oud... at (no spam) nononet.com> wrote:
[quote]Henry schrieb:
On 24 Oct, 05:18, karl <oud... at (no spam) nononet.com> wrote:
Henry schrieb:
On 23 Oct, 19:16, karl <oud... at (no spam) nononet.com> wrote:
HJ said definitely white noise.
HJ's second post in the thread suggested an approximation, and
that is what I replied to
So you have shown that a wrong approximation gives a wrong
result.
That is your assertion, not mine. And you need to back it up with
something more substantial than your current comments.
Apparently you can't show that the integral over your approximations
converges to the integral over white noise. If I say that it does not
converge to the integral over white noise, you suddenly say that you
never claimed that.
It is easy to see that the autocovariance function of your
approximations is always less equal 1. But if these would converge to
white noise, the autocovariance function at zero had to go to
infinity, since the autocovariance of white noise is the Dirac delta
function. So no convergence to white noise.
If you are going to say that white noise with a fixed finite
variance integrates to Brownian noise, I would interested to see
what you think the variance of the integral is.
Please explain the term "white noise with a fixed finite variance".
I guess you produce now your own definition of white noise.
The standard definition is that it is a generalized stationary
continuous-time stochastic process with mean zero whose spectral
density is constant (not zero) and
whose autocovariance function is a Dirac delta function. This you can
find in all textbooks.
There is no sense in discussing further if you now start using a private
definition of white noise different from the usual one given above.
[/quote]
You are correct that there is not point continuing this as we are
talking at cross purposes.
You are requiring white noise to be of infinite power, a physical
impossibility, while I was responding to HJ's question as posed. |
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