Errors:
On page 5, the subspace ${\cal G}$ of ${\cal H}$ should be assumed to be closed (so that it is also a Hilbert space) in several places.
On page 9, equation (12), there is a boldface $\mu$ missing after ${\bf V}^{-1}$.
On page 25, in equation (11), one should add the assumption that $K$ is absolutely integrable for its Fourier transform to be interpretable as an ordinary Lebesgue integral.
On page 26, line 9 from the bottom, the region of integration should be ${\Bbb R}^d$, not $R$.
On page 32, equation (17), there is a $\pi$ missing from the numerator of the right side and $\Gamma(2\nu-m+1)$ should be replaced by $\Gamma(2\nu-2m+1)$.
On page 33, line 2, replace $\alpha |t|^\nu$ by $(\alpha |t|)^\nu$. A similar error occurs on page 33, line 5.
On page 33, line 10, replace $U_2$ by $U_0$.
In Figure 4 on page 51, the dotted curve for $\nu=3$ is too low for all $t>0$. For example, the dotted curve should intersect the other curves around $t=2.8$.
On pages 70 and 239, Pannatier is misspelled.
On page 95, last line, replace $O(\delta^{\alpha-1})$ by $o(\delta^{\alpha-1}$.
The "reasonable conjecture" on the middle of page 120 about orthogonality of Gaussian measures when (20) does not hold is false. I have written a paper on this topic and I'll add a reference when available.
On page 157, line 12, replace $o(n_j^{-p})$ by $o(n_j^{-p/d})$.
The claim in Exercise 19 on page 175 that a certain linear combination of Fisher information matrices is positive semidefinite is false. As a consequence, the statement on page 179 that repeating the same pattern of observations for a stationary process at most doubles the Fisher information matrix is not justified, although it appears to often be true in practice.
On page 204, in Equation (38), there is a missing factor of 1/2 on the right hand side. The error is due to a missing term in the first approximation in (42) on page 45 that would cancel the last term in the second approximation in (42).
On page 218, the true value of rho is 6.124, not 1.624.
On page 233, last line, the second Z is in the wrong font.
On page 239, Matheron (1973) appeared in Advances in Applied Probability, not Journal of Applied Probability.
On page 242, the last page of Ying (1991) is 296, not 396.