Fractional Brownian motion
February 18, 2017 — February 18, 2017
probability
self similar
statistics
stochastic processes
time series
Nonstationary, (differently) self-similar generalisation of Brownian motion. Placeholder.
1 References
Brouste, Istas, and Lambert-Lacroix. 2016. “Conditional Fractional Gaussian Fields with the Package FieldSim.” R JOURNAL.
Dieker. 2004. “Simulation of Fractional Brownian Motion.” MSc Theses, University of Twente, Amsterdam, The Netherlands.
Emery. 2007. “Conditioning Simulations of Gaussian Random Fields by Ordinary Kriging.” Mathematical Geology.
Gaigalas. 2006. “A Poisson Bridge Between Fractional Brownian Motion and Stable Lévy Motion.” Stochastic Processes and Their Applications.
Kroese, and Botev. 2013. “Spatial Process Generation.” arXiv:1308.0399 [Stat].
Kroese, Taimre, and Botev. 2011. “Random Process Generation.” In Handbook of Monte Carlo Methods.
Norros, Mannersalo, and Wang. 1999. “Simulation of Fractional Brownian Motion with Conditionalized Random Midpoint Displacement.” Adv. Perf. Anal.
Nuzman, and Poor. 2000. “Linear Estimation of Self-Similar Processes via Lamperti’s Transformation.” Journal of Applied Probability.
Yin. 1996. “New Methods for Simulation of Fractional Brownian Motions.” Journal of Computational Physics.