Holonomic Modules Associated with Multivariate Normal Probabilities of Polyhedra

Moduli of regular holonomic D-modules with normal crossing singularities

This paper solves the global moduli problem for regular holonomic Dmodules with normal crossing singularities on a nonsingular complex projective variety. This is done by introducing a level structure (which gives rise to “pre-D-modules”), and then introducing a notion of (semi-)stability and applying Geometric Invariant Theory to construct a coarse moduli scheme for semistable pre-D-modules. A...

Moduli of Regular Holonomic -modules with Normal Crossing Singularities

Numerical Computation of Multivariate Normal Probabilities

The numerical computation of a multivariate normal probability is often a diicult problem. This article describes a transformation that simpliies the problem and places it into a form that allows eecient calculation using standard numerical multiple integration algorithms. Test results are presented that compare implementations of two algorithms that use the transformation, with currently avail...

Parallel Computation of Multivariate Normal Probabilities

We present methods for the computation of multivari-ate normal probabilities on parallel/ distributed systems. After a transformation of the initial integral, an approximation can be obtained using Monte-Carlo or quasi-random methods. We propose a meta-algorithm for asynchronous sampling methods and derive eecient parallel algorithms for the computation of MVN distribution functions, including ...

Semi–holonomic Verma Modules

Verma modules arise geometrically through the jets of homogeneous vector bundles. We consider in this article, the modules that arise from the semi-holonomic jets of a homogeneous vector bundle. We are particularly concerned with the case of a sphere under MMbius transformations. In this case there are immediate applications in the theory of conformally invariant diierential operators.