Sciweavers

Share
MOC
2002

The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension

9 years 11 months ago
The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension
Dimensionally unbounded problems are frequently encountered in practice, such as in simulations of stochastic processes, in particle and light transport problems and in the problems of mathematical finance. This paper considers quasi-Monte Carlo integration algorithms for weighted classes of functions of infinitely many variables, in which the dependence of functions on successive variables is increasingly limited. The dependence is modeled by a sequence of weights. The integrands belong to rather general reproducing kernel Hilbert spaces that can be decomposed as the direct sum of a series of their subspaces, each subspace containing functions of only a finite number of variables. The theory of reproducing kernels is used to derive a quadrature error bound, which is the product of two terms: the generalized discrepancy and the generalized variation. Tractability means that the minimal number of function evaluations needed to reduce the initial integration error by a factor is bounded...
Fred J. Hickernell, Xiaoqun Wang
Added 22 Dec 2010
Updated 22 Dec 2010
Type Journal
Year 2002
Where MOC
Authors Fred J. Hickernell, Xiaoqun Wang
Comments (0)
books