The joint distribution of the maximum and minimum of an AR(1) process

Consider a sequence of n observations from an autoregressive process of order 1 with maximum Mn and minimum mn. We give their joint cumulative distribution function first in terms of n repeated integrals and then, for the case, where the marginal distribution of the observations is absolutely continuous, as a weighted sum of nth powers of eigenvalues of a certain Fredholm kernel. This enables good approximations for the joint distribution when n repeated integrals is not a practical solution.