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Is the white noise a stochastic process?

0

$begingroup$

If $B_t$ is a Brownian motion, we commonly denote $xi(t)=dB_t$ as a white noise. But can it be considered as a stochastic process ? And if yes which law it follow ?

I'm not really sure how to interpret $dB_t$, but roughly speaking it looks like $dB_t=B_{t+dt}-B_tsim mathcal N(0,dtsigma ^2)$, but does it really make sense ? I'm not sure if $xi(t)sim mathcal N(0,dt sigma ^2)$ really make sense.

probability stochastic-processes

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asked Mar 25 at 9:53

user657324user657324

63610

$endgroup$

add a comment | 

0

$begingroup$

If $B_t$ is a Brownian motion, we commonly denote $xi(t)=dB_t$ as a white noise. But can it be considered as a stochastic process ? And if yes which law it follow ?

I'm not really sure how to interpret $dB_t$, but roughly speaking it looks like $dB_t=B_{t+dt}-B_tsim mathcal N(0,dtsigma ^2)$, but does it really make sense ? I'm not sure if $xi(t)sim mathcal N(0,dt sigma ^2)$ really make sense.

probability stochastic-processes

share|cite|improve this question

asked Mar 25 at 9:53

user657324user657324

63610

$endgroup$

add a comment | 

$begingroup$

If $B_t$ is a Brownian motion, we commonly denote $xi(t)=dB_t$ as a white noise. But can it be considered as a stochastic process ? And if yes which law it follow ?

I'm not really sure how to interpret $dB_t$, but roughly speaking it looks like $dB_t=B_{t+dt}-B_tsim mathcal N(0,dtsigma ^2)$, but does it really make sense ? I'm not sure if $xi(t)sim mathcal N(0,dt sigma ^2)$ really make sense.

probability stochastic-processes

share|cite|improve this question

asked Mar 25 at 9:53

user657324user657324

63610

$endgroup$

share|cite|improve this question

asked Mar 25 at 9:53

user657324user657324

63610

share|cite|improve this question

asked Mar 25 at 9:53

user657324user657324

63610

asked Mar 25 at 9:53

user657324user657324

63610

asked Mar 25 at 9:53

user657324user657324

63610