For 1000 equally spaced \(t\)-values in \((0,10]\) compute the FBM covariance matrix \(K\) and its Choleski factorization \(K=L^{\prime} L\). (If \(t=0\) is included, \(K\) is rank deficient, and the factorization may fail.) Thence compute \(Y=L^{\prime} Z\), where the components of \(Z\) are independent and identically distributed standard Gaussian, and plot the FBM sample path, \(Y_{t}\) against \(t\). Repeat this exercise for various values of \(v\) in \((0,1)\) and comment on the nature of FBM as a function of the Hurst coefficient.