Ian Melbourne's Publication List

Publications on Fast-Slow Systems

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. G. Gottwald and I. Melbourne. Time-reversibility and nonvanishing Lévy area.
   Nonlinearity 37 (2024) 075018 (12 pages at 1.5 months per page). (abstract, pdf file, journal version)

3. I. Chevyrev, P. K. Friz, A. Korepanov, I. Melbourne and H. Zhang. Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 2.
   Ann. Inst. H. Poincaré (B) Probab. Statist. 58 (2022) 1328-1350. (abstract, pdf file, published version)

4. A. Korepanov, Z. Kosloff and I. Melbourne. Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 1.
   Ann. Inst. H. Poincaré (B) Probab. Statist. 58 (2022) 1305-1327. (abstract, pdf file, published version)

5. M. Galton and I. Melbourne. Iterated invariance principle for slowly mixing dynamical systems.
   Ann. Inst. H. Poincaré (B) Probab. Statist. 58 (2022) 1284-1304. (abstract, pdf file, published version)

6. 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)

7. 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)

8. I. Chevyrev, P. K. Friz, A. Korepanov, I. Melbourne and H. Zhang. Multiscale systems, homogenization, and rough paths.
   Probability and Analysis in Interacting Physical Systems: In Honor of S.R.S. Varadhan, Berlin, August, 2016, eds. P. Friz et al. Springer Proc. in Maths. & Stat. 283 (2019) 17-42. (abstract, pdf file)

9. A. Korepanov, Z. Kosloff and I. Melbourne. Martingale-coboundary decomposition for families of dynamical systems.
   Annales de l'Institut Henri Poincaré / Analyse Non Lineaire 35 (2018) 859-885. (abstract, pdf file)

10. A. Korepanov, Z. Kosloff and I. Melbourne. Averaging and rates of averaging for uniform families of deterministic fast-slow skew product systems.
    Studia Math. 238 (2017) 59-89. (abstract, Online First pdf file)

11. D. Kelly and I. Melbourne. Deterministic homogenization for fast-slow systems with chaotic noise.
    J. Funct. Anal. 272 (2017) 4063-4102. (abstract, pdf file)

12. D. Kelly and I. Melbourne. Smooth approximation of stochastic differential equations.
    Annals of Probability 44 (2016) 479-520. (abstract, pdf file)

13. 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)

14. I. Melbourne and A. M. Stuart. A note on diffusion limits of chaotic skew product flows.
    Nonlinearity 24 (2011) 1361-1367. (abstract, pdf file, correction, April 2015, corrected version, April 2015)