A Taylor space for multivariate integration

Dick Josef ()
Additional contact information
Dick Josef: email:josi@maths.unsw.edu.au

Monte Carlo Methods and Applications, 2006, vol. 12, issue 2, 99-112

Abstract: In this paper we introduce reproducing kernel Hilbert spaces based on Taylor series. The unit ball of this space contains functions which are infinite at the boundary.We investigate multivariate integration in such spaces and show how functions in such spaces can be integrated with orderO(N−τ) for τ > 0 arbitrarily large, in spite of the unboundedness of the functions at the boundary. Further we prove that the Taylor space contains functions with infinite variance and hence the function space contains functions for which a simple Monte Carlo algorithm converges with probability one but convergence could be arbitrarily slow.

Date: 2006
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/156939606777488860 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:12:y:2006:i:2:p:99-112:n:4

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/mcma/html

DOI: 10.1515/156939606777488860

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().