Understanding Holder Continuity for Machine Learning research part7
- Approximation of SPDEs with Holder Continuous Drifts(arXiv)
Author : Jianhai Bao, Xing Huang, Chenggui Yuan
Abstract : : In this paper, exploiting the regularities of the corresponding Kolmogorov equations involved we investigate strong convergence of exponential integrator scheme for a range of stochastic partial differential equations, in which the drift term is Hölder continuous, and reveal the rate of convergence.
2.L1-optimal linear programming estimatorfor periodic frontier functions with Holder continuous derivative (arXiv)
Author : Alexander Nazin, Stephane Girard
Abstract : We propose a new estimator based on a linear programming method for smooth frontiers of sample points. The derivative of the frontier function is supposed to be Holder continuous.The estimator is defined as a linear combination of kernel functions being sufficiently regular, covering all the points and whose associated support is of smallest surface. The coefficients of the linear combination are computed by solving a linear programming problem. The L1- error between the estimated and the true frontier functionsis shown to be almost surely converging to zero, and the rate of convergence is proved to be optimal
