Ian Melbourne's Publication List

Publications on Lévy processes

  1. I. Chevyrev, A. Korepanov and I. Melbourne. Superdiffusive limits beyond the Marcus regime for deterministic fast-slow dynamical systems.
    Comm. Amer. Math. Soc. 4 (2024) 746-786. (abstract, pdf file)

  2. A. C. Freitas, J. Freitas, I. Melbourne and M. Todd. Convergence to decorated Lévy processes in non-Skorohod topologies for dynamical systems.
    Electron. J. Probab. 29 paper no. 170 (2024) 1-24. (abstract, pdf file)

  3. P. Jung, I. Melbourne, F. Pène, P. Varandas and H.-K. Zhang. Necessary and sufficient condition for M2-convergence to a Lévy process for billiards with cusps at flat points.
    Stoch. Dyn. 21 (2021) 2150024, 8 pages. (abstract, pdf file)

  4. G. Gottwald and I. Melbourne. Simulation of non-Lipschitz α-stable stochastic differential equations: a method based on deterministic homogenisation.
    Multiscale Modeling and Simulation 19 (2021) 665-687. (abstract, pdf file)

  5. I. Chevyrev, P. K. Friz, A. Korepanov and I. Melbourne. Superdiffusive limits for deterministic fast-slow dynamical systems.
    Probab. Theory Related Fields 178 (2020) 735-770. (abstract, pdf file)

  6. I. Melbourne and P. Varandas. Convergence to a Lévy process in the Skorohod M1 and M2 topologies for nonuniformly hyperbolic systems, including billiards with cusps.
    Commun. Math. Phys. 375 (2020) 653-678. (abstract, pdf file, View only of published version)

  7. G. Gottwald and I. Melbourne. On the detection of superdiffusive behaviour in time series.
    J. Stat. Mech. (2016) 123205 (14 pages) (abstract, pdf file)

  8. G. Gottwald and I. Melbourne. Central limit theorems and suppression of anomalous diffusion for systems with symmetry.
    Nonlinearity 29 (2016) 2941-2960. (abstract, pdf file)

  9. G. Gottwald and I. Melbourne. Broadband nature of power spectra for intermittent maps with summable and nonsummable decay of correlations.
    J. Phys. A 49 (2016) 174003 (17 pages) (abstract, pdf file)

  10. I. Melbourne and R. Zweimüller. Weak convergence to stable Lévy processes for nonuniformly hyperbolic dynamical systems.
    Ann. Inst. H. Poincaré Probab. Statist. 51 (2015) 545-556. (abstract, pdf file)

  11. G. Gottwald and I. Melbourne. Homogenization for deterministic maps and multiplicative noise.
    Proc. Roy. Soc. London A 469 (2013) 20130201 (abstract, pdf file, corrected version, April 2015)

  12. G. Gottwald and I. Melbourne. A Huygens principle for diffusion and anomalous diffusion in spatially extended systems.
    Proc. Natl. Acad. Sci. USA 110 (2013) 8411-8416. (abstract, pdf file) Supplementary information 1 (pdf file) Supplementary information 2 (pdf file)