represents fractional Brownian motion process with drift μ, volatility σ, and Hurst index h.
represents fractional Brownian motion process with drift 0, volatility 1, and Hurst index h.
- FractionalBrownianMotionProcess is also known as fractal Brownian motion or fractional Wiener process.
- FractionalBrownianMotionProcess is a continuous-time and continuous-state random process.
- FractionalBrownianMotionProcess is a Gaussian process with mean function and covariance function . It reduces to a WienerProcess for .
- FractionalBrownianMotionProcess allows μ to be any real number, σ to be any positive real number, and h to be a real number between 0 and 1.
- FractionalBrownianMotionProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.
Examplesopen allclose all
Basic Examples (3)
Basic Uses (6)
Process Slice Properties (5)
CentralMoment and its generating function:
Cumulant and its generating function:
Properties & Relations (4)
FractionalBrownianMotionProcess is not weakly stationary:
WienerProcess is a special case of fractional Brownian motion:
Neat Examples (3)
Wolfram Research (2012), FractionalBrownianMotionProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/FractionalBrownianMotionProcess.html.
Wolfram Language. 2012. "FractionalBrownianMotionProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FractionalBrownianMotionProcess.html.
Wolfram Language. (2012). FractionalBrownianMotionProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FractionalBrownianMotionProcess.html