Is the white noise a stochastic process? Announcing the arrival of Valued Associate #679:...
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Is the white noise a stochastic process?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Considering Brownian bridge as conditioned Brownian motionMaking a non-Martingale process a MartingaleTime integral of a stochastic processHow can we prove that the derivative of a generalized Hilbert space valued Brownian motion is a Gaussian white noise?What is “white noise” and how is it related to the Brownian motion?Intutitive understanding of the law of a stochastic processUnderstand different types of white noise processStochastic Differential of $e^{B(t)-frac{1}{2}t}$Integrate function of a Gaussian white noise process w.r.t. time?In probability, what is exactly a noise and a white noise?
$begingroup$
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
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
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
asked Mar 25 at 9:53
user657324user657324
63610
$endgroup$
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
probability stochastic-processes
asked Mar 25 at 9:53
user657324user657324
63610
asked Mar 25 at 9:53
user657324user657324
63610
asked Mar 25 at 9:53
user657324user657324
63610
asked Mar 25 at 9:53
user657324user657324
63610
asked Mar 25 at 9:53
user657324user657324
63610
63610
add a comment |
add a comment |
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