integrate_fractional_brownian_trajectory: Generate integrate fractional Brownian motion with a random...

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

Description

This function generates a realization of an 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

integrate_fractional_brownian_trajectory(M, H, sigma, 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. As we return its integrated version, the true Hurst will be 1 + H.
sigma	A vector of numeric, 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

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