Continuous-time stochastic process W_t with (i) W_0 = 0, (ii) independent increments, (iii) W_t - W_s sim mathcalN(0, t-s), and (iv) continuous but almost-surely nowhere-differentiable paths. Quadratic variation langle W rangle_t = t — the property that makes Itô calculus distinct from ordinary calculus, since (dW_t)^2 = dt does not vanish. The basic noise driver of every continuous-time finance model (GBM, Vasicek, Heston, HJM).