Like this?
monoStochProc[init_, window_, n_] := NestList[RandomReal[{# window, #}] &, init, n] ListLogPlot[monoStochProc[10^11, 0.7, 59], Joined -> True, Mesh -> All, Filling -> Axis, Frame -> True]
Thank you for your answer!
Yes, that is what I wanted. It didn't come to mind
