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I'm working through a proof showing that the Wiener process is non differentiable given as follows enter image description here

I am not quite sure where the 2 in front of the integral stems from though. Any help would be highyly appreciated :)

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    – user191954
    Commented Jul 16, 2018 at 9:19
  • $\begingroup$ Hi Chair, Thanks for the heads up - I'll keep that in mind :-) $\endgroup$
    – user469216
    Commented Jul 16, 2018 at 9:38
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    $\begingroup$ I see you've left a 'thanks' comment under LonelyProf's answer. If that answer helped you enough, it's a better idea to mark it as accepted (I think you'll see a grey tick mark or something next to that answer). "thank-you" comments are usually deleted here because they're considered to be noise. $\endgroup$
    – user191954
    Commented Jul 16, 2018 at 9:43

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I imagine that it is because the distribution of $\Delta B$ ranges from $-\infty$ to $+\infty$ and we are seeking values of $|\Delta B| > A\Delta t$. The integral is symmetric, so the range is changed to just cover the positive interval, and the result is doubled.

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