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The convergence of $$F$$-variation for Gaussian random fields. (English. Ukrainian original) Zbl 0955.60035
Theory Probab. Math. Stat. 60, 113-123 (2000); translation from Teor. Jmovirn. Mat. Stat. 60, 102-111 (1999).
For any $$F: R\to R$$ and a random field $$\xi(t)$$, $$t\in[0,1]^d,$$ the F-variation is defined as $V_n(F)=a_n^{-d}\sum F((\triangle \xi_k/E\triangle\xi_k)^2)^{1/2},$ where $$\triangle\xi_k$$ are increments of the field $$\xi$$ on a uniform partitioning of $$[0,1]^d.$$ The paper deals with the Baxter-type theorems for $$V_n(F)$$. Conditions are presented under which $$V_n(F)$$ converges to some nonrandom constant $$C\not=0$$ as $$n\to\infty$$. A Chentsov field and a multiparameter fractional Brownian motion are considered as examples.
MSC:
 60G15 Gaussian processes 60G60 Random fields