Description
1. Simulate a Gaussian process with zero mean and following covariance
structures with T = [0, 1]. (10 points)
(a) K(s, t) = e
−16(s−t)
2
(b) K(s, t) = min(s, t)
2. Suppose that A and B each start with a stake of 10, and bet 1 on consecutive coin flips. The game ends when either one of the players has all the
money. Let Sn be the fortune of player A at time n. Then {Sn, n ≥ 0} is
a symmetric random walk with absorbing barriers at 0 and 20. Simulate a
realization of the process {Sn, n ≥ 0} and plot Sn vs the time index from
time 0 until a barrier is reached. (10 points)
1
