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A Taylor space for multivariate integration

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  • Dick Josef

    (email:josi@maths.unsw.edu.au)

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.

Suggested Citation

  • Dick Josef, 2006. "A Taylor space for multivariate integration," Monte Carlo Methods and Applications, De Gruyter, vol. 12(2), pages 99-112, April.
    • Handle: RePEc:bpj:mcmeap:v:12:y:2006:i:2:p:99-112:n:4
    DOI: 10.1515/156939606777488860
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