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Twisted modules and co-invariants for commutative vertex algebras of jet schemes
Let Z⊂k be an affine scheme over \C and \J Z its jet scheme. It is well-known that \mathbb{C}[\J Z], the coordinate ring of \J Z, has the structure of a commutative vertex algebra. This paper develops the orbifold theory for \mathbb{C}[\J Z]. A finite-order linear automorphism g of Z acts by vertex algebra automorphisms on \mathbb{C}[\J Z]. We show that \mathbb{C}[\J^g Z], where \J^g Z is the scheme of g--twisted jets has the structure of a g-twisted \mathbb{C}[\J Z] module. We consider spaces of orbifold coinvariants valued in the modules \mathbb{C}[\J^g Z] on orbicurves [Y/G], with Y a smooth projective curve and G a finite group, and show that these are isomorphic to ℂ[ZG]
On the discretization of backward doubly stochastic differential equations
In this paper, we are dealing with the approximation of the process (Y,Z)
solution to the backward doubly stochastic differential equation with the
forward process X . After proving the L2-regularity of Z, we use the Euler
scheme to discretize X and the Zhang approach in order to give a discretization
scheme of the process (Y,Z)
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