The CumulativeSum is a utility routine for computing cumulative sums of data.

The CumulativeProduct is a utility routine for computing cumulative products of data.

The first parameter X is a data sample - given as e.g. a Vector.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$N≔10$

$N≔10$

$h≔\frac{1.}{N-1}$

$h≔0.1111111111$

$\mathrm{\sigma }≔0.2\;$$r≔0.1$

$\mathrm{\sigma }≔0.2$

$r≔0.1$

$U≔\mathrm{RandomVariable}\left(\mathrm{Normal}\left(0\,\mathrm{\sigma }\mathrm{sqrt}\left(h\right)\right)\right)$

$U≔\mathrm{\_R}$

$R≔\mathrm{Sample}\left(\exp \left(rh-\frac{{\mathrm{\sigma }}^{2}h}{2}\right)\exp \left(U\right)\,N\right)$

$R≔\left[\begin{array}{cccccccccc}0.939313440198753& 0.990244516766144& 1.05043038223201& 0.981220475406314& 0.964074854341808& 1.02045245942057& 1.03782546004108& 0.971126773289737& 0.994968315345709& 0.994468626738408\end{array}\right]$

$S≔\mathrm{CumulativeSum}\left(R\right)$

$S≔\left[\begin{array}{cccccccccc}0.939313440198753& 1.92955795696490& 2.97998833919691& 3.96120881460322& 4.92528366894503& 5.94573612836560& 6.98356158840668& 7.95468836169642& 8.94965667704213& 9.94412530378054\end{array}\right]$

$P≔\mathrm{CumulativeProduct}\left(R\right)$

$P≔\left[\begin{array}{cccccccccc}0.939313440198753& 0.930149983681559& 0.977057802891718& 0.958709121852860& 0.924267357006458& 0.943170897619390& 0.978846770719206& 0.950584305993622& 0.945801265528544& 0.940569685697619\end{array}\right]$

$\mathrm{LineChart}\left(\left[S\,P\right]\,\mathrm{legend}=\left[''Cumulative\; Sum''\,''Cumulative\; Product''\right]\right)$