Estimation of parameters of homogeneous Gaussian random fields (Q2722140)

\textit{P. Lévy} [Am. J. Math. 62, 487-550 (1940; Zbl 0024.13906)] proved that for a standard Brownian motion \(\{w(t);\;t\in [0,1]\}\) the sum of squares of increments tends in mean square (and, under additional conditions, almost sure) to \(1\) under the condition that the diameter of partition of the interval \([0,1]\) tends to zero. \textit{G. Baxter} [Proc. Am. Math. Soc. 7, 522-527 (1956; Zbl 0070.36304)] generalized this result for a wide class of Gaussian random fields. Such limit theorems are called now Baxter-type theorems or Lévy-Baxter's theorems.NEWLINENEWLINENEWLINEIn this work, on the basis of limit theorems for quadratic variation, a consistent estimate for the parameters of a Gaussian homogeneous random field from a certain class is constructed. Confidence ellipsoids for the estimates of this sort are found.