Prove formulas XXXXXXXXXXand XXXXXXXXXXProve that the autocorrelation of Z (the correlation of Z(t) with Z(t +u)) is   Explain (heuristically) why   And   and use this to derive formulas XXXXXXXXXXand...

Prove formulas (11.7) and (11.8). Prove that the autocorrelation of Z (the correlation of Z(t) with Z(t +u)) is

Explain (heuristically) why

And

and use this to derive formulas (11.14) and (11.15). Furthermore, prove that

Note that this is independent of the Laplace exponent, that is, of what subordinator you use in the frailty formulation.