a and b are known constants.) Suppose we have generated a number of points W(0), W(1), W(2), W(3), etc. of a Wiener process path by computer simulation. It is now desired to fill in additional points in the interval [0,T], that is to interpolate between the already generated points W(0) and W(T). The solution is to use a Brownian bridge that is required to go through the values W(0) and W(T). General case For the general case when B(t1) = a and B(t2) = b, the distribution of B at time t ∈ (t1, t2) is normal, with mean and variance and the covariance between B(s) and B(t), with s < t is References Wiener process Empirical process