Hi Frederico

Brilliant article and images. A central part of your analysis is the construction of random walks that either end at the same point or 1-D random walks in time that end at zero. However there is already an inbuilt Mathematica functions for this, specifically the BrownianBridgeProcess[] function. Using BrownianBridgeProcess[sigma, {t1,a},{t2,b}] you can define a random walk with volatility sigma, that starts at time t1 at value a and returns to value b at a later time t2. By putting t1 = 0 and a =b =0 you can get your time series process going from 0 to 0 along with its time related behavior and its distribution at each step of the process.

Regards Michael