I admit that I assumed that "geometric browning motion" was just "a random walk with more extreme movements when it goes away from the starting place," and that

I admit that I assumed that "geometric browning motion" was just "a random walk with more extreme movements when it goes away from the starting place," and that was wrong. What geometric browning motion in fact is, with some handwaving simplicity, is exponential growth with some jitter. I will note that "stocks are priced via geometric browning motion" would satisfy the EMH. And that the underlying growth trend of GBM, in a real world, is, like, "the stock market actually values real things about the company that you can find out, but which other people have already found out."