Suppose X(t) denotes the stock level of a certain product at time t and the holding cost up to time t is Y (t) = h ! t 0 X(s) ds, where h is the cost per unit time of holding one unit in inventory....

Suppose X(t) denotes the stock level of a certain product at time t and the holding cost up to time t is Y (t) = h ! t 0 X(s) ds, where h is the cost per unit time of holding one unit in inventory. Show that if X is a Brownian motion B, then the mean and covariance functions of Z areFind the mean and covariance functions of Y if X(t) = x + μt + σB(t), a Brownian motion with drift; or if X is a compound Poisson process as in the preceding problem.