N ( μ μ , σ σ 2 ) denotes the normal distribution with expected value μ and variance σ. The condition that it has independent increments means that if 0 ≤ ≤ s 1 < t 1 ≤ ≤ s 2 < t 2 then W t 1 − − W s 1 and W t 2 − − W s 2 are independent random variables. In addition, for some filtration F t , W t is F t measurable for all t ≥ ≥ 0 .