Finite Difference Methods for the generator of 1D asymmetric alpha-stable Lévy motions

Yanghong Huang, Xiao Wang

    Research output: Contribution to journalArticlepeer-review

    87 Downloads (Pure)

    Abstract

    Several finite difference methods are proposed for the infinitesimal generator of 1D asymmetric α-stable Lévy motions, based on the fact that the operator becomes a multiplier in the spectral space. These methods take the general form of a discrete convolution, and the coefficients (or the weights) in the convolution are chosen to approximate the exact multiplier after appropriate transform. The accuracy and the associated advantages/disadvantages are also discussed, providing some guidance on the choice of the right scheme for practical problems, like in the calculation of mean exit time for random processes governed by general asymmetric α-stable motions.
    Original languageEnglish
    JournalComputational Methods in Applied Mathematics
    Volume18
    Issue number1
    Early online date2 Sep 2017
    DOIs
    Publication statusPublished - 2017

    Keywords

    • Finite difference methods
    • Levy processes
    • Pseudodifferential operators

    Fingerprint

    Dive into the research topics of 'Finite Difference Methods for the generator of 1D asymmetric alpha-stable Lévy motions'. Together they form a unique fingerprint.

    Cite this