Abstract tubes associated with perturbed polyhedra with applications to multidimensional normal probability computations

@article{Kuriki2011AbstractTA,
  title={Abstract tubes associated with perturbed polyhedra with applications to multidimensional normal probability computations},
  author={Satoshi Kuriki and Tetsuhisa Miwa and Anthony J. Hayter},
  journal={arXiv: Computation},
  year={2011}
}
Let $K$ be a closed convex polyhedron defined by a finite number of linear inequalities. In this paper we refine the theory of abstract tubes (Naiman and Wynn, 1997) associated with $K$ when $K$ is perturbed. In particular, we focus on the perturbation that is lexicographic and in an outer direction. An algorithm for constructing the abstract tube by means of linear programming and its implementation are discussed. Using the abstract tube for perturbed $K$ combined with the recursive… 

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