3.5 Let {XI(t) t d} be an intrinsic random field (of intrinsic order k =...

3.5 Let {XI(t) ∶ t ∈ ℝd} be an intrinsic random field (of intrinsic order k = 0)

with semivariogram ????(h). Given a fixed vector h0 ∈ ℝd, define a new random field by Y(t) = XI(t) − XI(t − h0).

Using (3.4) show that {Y(t)} is stationary and that its covariance function takes the form cov{Y(t), Y(s)} = ????(t − s − h0) + ????(s − t − h0) − 2????(t − s).