generate_fractional_brownian: Generate a list of fractional Brownian trajectory.

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

Description

This function generates a list of realizations 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].

Usage

generate_fractional_brownian(
  N = 100,
  M = 10,
  H = 0.5,
  sigma = 0.05,
  pdf = NULL,
  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
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 σ

Examples

generate_fractional_brownian(100, 50, 0.7, 0.1)
generate_fractional_brownian(100, 50, 0.5, 0.05, pdf = rnorm)

StevenGolovkine/SmoothCurves documentation built on Nov. 14, 2021, 1:12 p.m.