I have been studying brownian motion for my undergraduate capstone project, and I have been looking at the range of the values that brownian motion takes on. To get a computational idea of what is going on, I wrote a matlab script that would run 100,000 simulations of brownian motion on t=[0,1] and save the range of each run. I then made a histogram of the ranges, and I have been looking to see if they follow some known PDF. I was wondering if anyone here could help me figure out what this distribution might be. I have scaled the Y axis to make it a PDF instead of leaving it as a count like it would be in a histogram.
