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I am confused about the relation between the white noise and Brownian motion.

The white nose $W(t)$ is formally regarded as the derivative of a Brownian motion B(t), i.e. $W(t) = dB(t)/dt$. However, the Brownian motion $B(t)$ is nowhere differentiable.

Is there any interpretation for these conflicting statements.

Bilal Jafar Karaki
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    Nowhere differentiable locally bounded functions are locally integrable and therefore have distributional derivatives – Calvin Khor Jul 11 '20 at 23:48
  • A question after almost 9 years! Does it mean that the writing SDE $$ dX(t) = \mu dt + \sigma dB(t), $$ is not mathematically correct? – Denis Aug 14 '20 at 10:10

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