Let X be a Brownian motion directed by η. Suppose the process η has stationary independent nonnegative increments and E[e−αη(t)] = ψ(α)t , where ψ(α) = E[e −αη (1)]. Determine the moment generating...

Let X be a Brownian motion directed by η. Suppose the process η has stationary independent nonnegative increments and E[e−αη(t)] = ψ(α)t , where ψ(α) = E[e^−αη(1)]. Determine the moment generating function of X(1) (as a function of ψ) and show that X has stationary independent increments.