Fractional Brownian motion

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

Brouste, Alexandre, Jacques Istas, and Sophie Lambert-Lacroix. 2016. “Conditional Fractional Gaussian Fields with the Package FieldSim.” R JOURNAL 8 (1): 38–47. http://perso.univ-lemans.fr/~abrouste/work/BIL15.pdf.

Dieker, Ton. 2004. “Simulation of Fractional Brownian Motion.” MSc Theses, University of Twente, Amsterdam, the Netherlands. http://www.columbia.edu/~ad3217/fbm/thesisold.pdf.

Emery, Xavier. 2007. “Conditioning Simulations of Gaussian Random Fields by Ordinary Kriging.” Mathematical Geology 39 (6): 607–23. https://doi.org/10.1007/s11004-007-9112-x.

Gaigalas, Raimundas. 2006. “A Poisson Bridge Between Fractional Brownian Motion and Stable Lévy Motion.” Stochastic Processes and Their Applications 116 (3): 447–62. https://doi.org/10.1016/j.spa.2005.10.003.

Kroese, Dirk P., and Zdravko I. Botev. 2013. “Spatial Process Generation,” August. http://arxiv.org/abs/1308.0399.

Kroese, Dirk P., Thomas Taimre, and Zdravko I. Botev. 2011. “Random Process Generation.” In Handbook of Monte Carlo Methods, 153–223. John Wiley & Sons, Inc. http://onlinelibrary.wiley.com/doi/10.1002/9781118014967.ch5/summary.

Norros, Ilkka, Petteri Mannersalo, and Jonathan L. Wang. 1999. “Simulation of Fractional Brownian Motion with Conditionalized Random Midpoint Displacement.” Adv. Perf. Anal. 2: 77–101. https://project.inria.fr/fraclab/files/2016/01/Simulation-of-Fractional-Brownian-Motion-with-Conditionalized-Random-Midpoint-Displacement.pdf.

Nuzman, Carl J., and H. Vincent Poor. 2000. “Linear Estimation of Self-Similar Processes via Lamperti’s Transformation.” Journal of Applied Probability 37 (2): 429–52. https://doi.org/10.1239/jap/1014842548.

Yin, Z. -M. 1996. “New Methods for Simulation of Fractional Brownian Motions.” Journal of Computational Physics 127 (1): 66–72. https://doi.org/10.1006/jcph.1996.0158.