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    Twisted modules and co-invariants for commutative vertex algebras of jet schemes

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    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

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    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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