For generically étale morphisms of varieties, a new relative Mather discrepancy function on arc spaces computes the kernel dimension of the induced arc-space map, and the new \hat K-equivalence preserves motivic classes in arbitrary characteristic.
Revisiting Stochastic Collocation with Exponential Splines for an Arbitrage-Free Interpolation of Option Prices
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abstract
We revisit the stochastic collocation method using the exponential of a quadratic spline. In particular, we look in details whether it is more appropriate to fix the ordinates and optimize the abscissae of an interpolating spline or to fix the abscissae and optimize the parameters of a B-spline representation.
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Relative Mather discrepancy on arc spaces
For generically étale morphisms of varieties, a new relative Mather discrepancy function on arc spaces computes the kernel dimension of the induced arc-space map, and the new \hat K-equivalence preserves motivic classes in arbitrary characteristic.