AI & ML
Ignoring Blow-Ups for Approximations
arXiv cs.NA0 views
arXiv:2611.08208v1 Announce Type: cross Abstract: It is well known that for SDEs with non-Lipschitz coefficients, the Euler scheme can fail to converge in an Lp sense. It is also widely observed that convergence fails only due to rare explosive trajectories, that distort the expectation. In this work we demonstrate that almost any method of removing these rare explosive trajectories leads to convergence in a suitable strong and weak sense. We apply this framework to coefficients that grow faster than linearly at infinity and Lennard-Jones type coefficients that explode like a reciprocal power on a compact set.
Source：https://arxiv.org/abs/2611.08208PreviousContinuous Space-Time Finite Element Simulations for Biomedical Flows with Large Boundary Motion and Time-PeriodicityNextData-driven discovery of intrinsic Lie point symmetries of differential equation systems
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