Description

Stochastic - A collection of stochastic processes.

Stochastic::Fbm

The Stochastic::Fbm function takes three arguments:

1. The Hurst parameter (hurst)
2. The length of the time series (length)
3. A delta parameter that scales the increments. Optional

It generates a fractional Brownian motion using the covariance matrix and Cholesky decomposition method.

The covariance matrix is created based on the Hurst parameter, and the Cholesky decomposition is performed on this matrix.

A vector of Gaussian random variables is generated using the randn function, which uses the Box-Muller method.

The fractional Brownian motion path is computed as the product of the Cholesky matrix and the vector of random variables.

The path is then returned as an array.

Usage

To use this script, set your Hurst parameter and time length, call the Stochastic::Fbm#sample function, and use or print the generated path as needed.

hurst_parameter = 0.75
time_length = 1000
fbm_path = Stochastic::Fbm.new(hurst_parameter, time_length)

# Print or use the fbm_path
fbm_path.sample.each_with_index do |val, index|
  puts "t#{index}: #{val}"
end