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)
Generalizations & Extensions (1)
Properties & Relations (4)
Neat Examples (3)
WienerProcess FractionalGaussianNoiseProcess RandomWalkProcess BrownianBridgeProcess GeometricBrownianMotionProcess OrnsteinUhlenbeckProcess NormalDistribution BinormalDistribution MultinormalDistribution