Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1147200 | Journal of Multivariate Analysis | 2006 | 16 Pages |
Abstract
We consider short asymptotic expansions for the probability of a sum of i.i.d. random elements to hit a ball in a Hilbert space H. The error bound for the expansion is of order O(n-1). It depends on the first 12 eigenvalues of the covariance operator only. Moreover, the bound is non-uniform, i.e. the accuracy of the approximation becomes better as the distance between a boundary of the ball and the origin in H grows.
Related Topics
Physical Sciences and Engineering
Mathematics
Numerical Analysis