between $t_0$ and $t$. Using Eq. (\[eq:shift\]) together with the distribution (\[eq:proba\]), the probability that the size of the shift in $\delta f$ induced by a fluctuation at time $t_1$ is less than some $F$ reads P(f&lt;F;t\_1)=C\_1( 1- ). We shall always assume that $F$ is finite, and the ordering $t,t-t_1,t_1\gg 1$. The probability distribution of $f$ then reads p(f;t\_1)=|\_[F=f]{}= . \[eq:pf01\] The rate of the fluctuations is assumed constant in time, thus the distribution of $f$ results from a simple integration over $t_1$ from $t_0$ to $t$ with uniform measure. It reads p(f)=2CC\_1   . \[eq:pf1\]

Exactly in the same way, we may compute the probability distribution of $f$ when the fluctuation occurs at a time smaller than $t_0$. In this case, the effect on $f$ of a fluctuation of size $\delta$ reads f=. Using the same method, we find p(f)=2C C\_1 ( 1- )   . \[eq:pf2\] The integral over $t_1$ which has to be performed to arrive at these expressions is dominated by values of $t_1$ of the order of $t_0$. This helps us to understand a posteriori why we were allowed to drop terms of order $1/\sqrt{t}$ and $1/\sqrt{t_1}$ in Eqs. (\[eq:Y0\]) and (\[eq:Xdelta\]), respectively, although we were 