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Multilevel lattice-based kernel approximation for elliptic PDEs with random coefficients
Alexander D. Gilbert, Michael B. Giles, Frances Y. Kuo +2
This paper introduces a multilevel kernel-based approximation method to estimate efficiently solutions to elliptic partial differential equations (PDEs) with periodic random coeffi…
Density estimation for elliptic PDE with random input by preintegration and quasi-Monte Carlo methods
Alexander D. Gilbert, Frances Y. Kuo, Abirami Srikumar
In this paper, we apply quasi-Monte Carlo (QMC) methods with an initial preintegration step to estimate cumulative distribution functions and probability density functions in uncer…
Comparison of Two Search Criteria for Lattice-based Kernel Approximation
Frances Y. Kuo, Weiwen Mo, Dirk Nuyens +2
The kernel interpolant in a reproducing kernel Hilbert space is optimal in the worst-case sense among all approximations of a function using the same set of function values. In thi…
Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation
Alexander D. Gilbert, Frances Y. Kuo, Ian H. Sloan +1
In this paper we propose and analyse a method for estimating three quantities related to an Asian option: the fair price, the cumulative distribution function, and the probability…