Finance, Mathematics, Brownian Motion, Financial Engineering, Mathematical Finance.
pretend we have an asset W whose accumulative return rate from time 0 to t is W(t). Suppose ∆t > 0 and is the unit time, then ∆W(t)=W(t+∆t) - W(t) means the return in time interval ∆t. We call the ∆W the increment, the return you got. Thus ∆W(t) means the increment at time t. W(0)=0 as the first