The process for the stock price in equation is

$\backslash$Delta S$=\backslash$mu S $\backslash$Delta t$+\backslash$sigma S $\backslash$epsi $(\backslash$Delta t$)$

where $\backslash$mu and $\backslash$sigma are constant. Explain carefully the difference between this model and each of the following:

$[\backslash$Delta S$=\backslash$mu $\backslash$Delta t$+\backslash$sigma $\backslash$epsi $(\backslash$Delta t$)$; $\backslash$Delta S$=\backslash$mu S $\backslash$Delta t$+\backslash$sigma $\backslash$epsi $(\backslash$Delta t$)$; $\backslash$Delta S$=\backslash$mu $\backslash$Delta t$+\backslash$sigma S $\backslash$epsi $(\backslash$Delta t$)]$

Why is the model in equation

$\backslash$Delta S$=\backslash$mu S $\backslash$Delta t$+\backslash$sigma S $\backslash$epsi $(\backslash$Delta t$)$

a more appropriate model of stock price behavior than any of these three alternatives?