Generate fractional Brownian motion with a random noise

Source: R/generate_data.R

This function generates a realization of a fractional Brownian motion with random noise. The increments of a fractional Brownian motion are not independent. A fractional Brownian motion is characterized by a parameter \(H\), named Hurst coefficient. We define it on \([0, 1]\).

fractional_brownian_trajectory(M, H, sigma, pdf = NULL, L = 1)

Arguments

M

An integer, expected number of points in the trajectory. The number of points follows a Poisson distribution with mean \(M\).
H

Numeric, Hurst coefficient. \(0 < H < 1\)
sigma

A vector of numeric, standard deviation of the noise to add to the fractional Brownian motion.
pdf

Function, probability density function for the sampling points.
L

Numeric, multiplicative constant.

Value

A tibble containing the following elements:

  • ...1 The sampling points

  • ...2 The true trajectory

  • ...3 The trajectory contaminated by noise with standard deviation \(\sigma\)