Holonomic modules associated with multivariate normal probabilities of polyhedra

  title={Holonomic modules associated with multivariate normal probabilities of polyhedra},
  author={Tamio Koyama},
  journal={arXiv: Classical Analysis and ODEs},
  • Tamio Koyama
  • Published 27 November 2013
  • Mathematics
  • arXiv: Classical Analysis and ODEs
The probability content of a convex polyhedron with a multivariate normal distribution can be regarded as a real analytic function. We give a system of linear partial differential equations with polynomial coefficients for the function and show that the system induces a holonomic module. The rank of the holonomic module is equal to the number of nonempty faces of the convex polyhedron, and we provide an explicit Pfaffian equation (an integrable connection) that is associated with the holonomic… 

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