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Spectral Method for the Fractional Laplacian in 2D and 3D
Kailai Xu, Eric Darve
A spectral method is considered for approximating the fractional Laplacian and solving the fractional Poisson problem in 2D and 3D unit balls. The method is based on the explicit f…
Efficient Numerical Method for Models Driven by Lévy Process via Hierarchical Matrices
Kailai Xu, Eric Darve
Modeling via fractional partial differential equations or a Lévy process has been an active area of research and has many applications. However, the lack of efficient numerical com…
Calibrating Multivariate Lévy Processes with Neural Networks
Kailai Xu, Eric Darve
Calibrating a Lévy process usually requires characterizing its jump distribution. Traditionally this problem can be solved with nonparametric estimation using the empirical charact…
Isogeometric Collocation Method for the Fractional Laplacian in the 2D Bounded Domain
Kailai Xu, Eric Darve
We consider the isogeometric analysis for fractional PDEs involving the fractional Laplacian in two dimensions. An isogeometric collocation method is developed to discretize the fr…