Dependence on the dimension for complexity of approximation of random fields
- Serdyukova, Nora
2010 Mathematics Subject Classification
- 41A63 60G60 60G15, 41A58
- Gaussian processes, random fields, Karhunen-Loève expansion, linear approximation error, information-based complexity, tractability, curse of dimensionality, multivariate linear problems
We consider the $e $-approximation by $n$-term partial sums of the Karhunen-Loève expansion to $d$-parametric random fields of tensor product-type in the average case setting. We investigate the behavior, as $dto infty$, of the information complexity $n(e,d)$ of approximation with error not exceeding a given level $e$. It was recently shown by M. A. Lifshits and E. V. Tulyakova that for this problem one observes the curse of dimensionality (intractability) phenomenon. The aim of this paper is to give the exact asymptotic expression for $n(e,d)$.
- Theory Probab. Appl., 54 (2010) pp. 272--284.