The Living Thing / Notebooks : Fractional Brownian Motion

Nonstationary, self-similar generalisation of Brownian motion. Handy.

Refs

BrIL16
Brouste, A., Istas, J., & Lambert-Lacroix, S. (2016) Conditional Fractional Gaussian Fields with the Package FieldSim. R JOURNAL, 8(1), 38–47.
Diek04
Dieker, T. (2004) Simulation of fractional Brownian motion. MSc Theses, University of Twente, Amsterdam, The Netherlands.
Emer07
Emery, X. (2007) Conditioning Simulations of Gaussian Random Fields by Ordinary Kriging. Mathematical Geology, 39(6), 607–623. DOI.
Gaig06
Gaigalas, R. (2006) A Poisson bridge between fractional Brownian motion and stable Lévy motion. Stochastic Processes and Their Applications, 116(3), 447–462. DOI.
KrBo13
Kroese, D. P., & Botev, Z. I.(2013) Spatial process generation. arXiv:1308.0399 [Stat].
KrTB11
Kroese, D. P., Taimre, T., & Botev, Z. I.(2011) Random Process Generation. In Handbook of Monte Carlo Methods (pp. 153–223). John Wiley & Sons, Inc.
NoMW99
Norros, I., Mannersalo, P., & Wang, J. L.(1999) Simulation of fractional Brownian motion with conditionalized random midpoint displacement. Adv. Perf. Anal., 2, 77–101.
NuPo00
Nuzman, C. J., & Poor, H. V.(2000) Linear estimation of self-similar processes via Lamperti’s transformation. Journal of Applied Probability, 37(2), 429–452. DOI.
Yin96
Yin, Z.-M. (1996) New methods for simulation of fractional Brownian motions. Journal of Computational Physics, 127(1), 66–72. DOI.