I'm trying to do some research on the modelling of asset pathways and am struggling to understand how the stochastic differential equation dS=S(σdX + μdt) is classified?
I know that it is a lognormal random walk and that dX is a stochastic process but I have also seen that this equation is a Geometric Brownian motion. This is were I get confused as I don't understand the explicit difference between a lognormal random walk and a Geometric Brownian motion or how this equation can be both!
Any help is extremely appreciated and apologies if any of the above is incorrect:))