generate_integrate_fractional_brownian: Generate a list of integrate fractional Brownian trajectory.

In StevenGolovkine/denoisr: Nonparametric Kernel Smoothing Methods for Functional Data

Description

This function generates a list of realizations of a integrate fractional Brownian motion with random noise. The increments of a integrate fractional Brownian motion are not independent. An integrate fractional Brownian motion is characterized by a parameter H, named Hurst coefficient. We define it on [0, 1].

Usage

generate_integrate_fractional_brownian(
  N = 100,
  M = 10,
  H = 0.5,
  sigma = 0.05,
  L = 1
)

Arguments

N	An integer, number of curves to simulate.
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. As we return its integrated version, the true Hurst will be 1 + H.
sigma	A vector of numerics, standard deviation of the noise to add to the fractional Brownian motion.
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 σ

Examples

generate_integrate_fractional_brownian(100, 50, 0.7, 0.1)
generate_integrate_fractional_brownian(100, 50, 0.5, 0.05, 2)

StevenGolovkine/denoisr documentation built on Nov. 15, 2021, 8:44 a.m.