I'm currently studying brownian motion and came across two kinds of geometric brownian motion. http://homepage.univie.ac.at/kujtim.avdiu/dateien/BrownianMotion.pdf (page 14) http://www.math.unl.edu/~sdunbar1/MathematicalFinance/Lessons/StochasticCalculus/GeometricBrownianMotion/geometricbrownian.pdf (page 2)
I can't see the difference between the two formulas. I prefer the 2nd one since it seems simpler but both give different kind of expectation and variance and this is making it confusing for me to understand.
Can anyone explain the difference between the two?