Fractional Brownian motion



Nonstationary, (differently) self-similar generalisation of Brownian motion. Placeholder.

References

Brouste, Alexandre, Jacques Istas, and Sophie Lambert-Lacroix. 2016. Conditional Fractional Gaussian Fields with the Package FieldSim.” R JOURNAL 8 (1): 38–47.
Dieker, Ton. 2004. Simulation of Fractional Brownian Motion.” MSc Theses, University of Twente, Amsterdam, The Netherlands.
Emery, Xavier. 2007. Conditioning Simulations of Gaussian Random Fields by Ordinary Kriging.” Mathematical Geology 39 (6): 607–23.
Gaigalas, Raimundas. 2006. A Poisson Bridge Between Fractional Brownian Motion and Stable Lévy Motion.” Stochastic Processes and Their Applications 116 (3): 447–62.
Kroese, Dirk P., and Zdravko I. Botev. 2013. Spatial Process Generation.” arXiv:1308.0399 [Stat], August.
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.
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.
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.
Yin, Z. -M. 1996. New Methods for Simulation of Fractional Brownian Motions.” Journal of Computational Physics 127 (1): 66–72.

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