FBm: Simulation of fractional Brownian motion

In Rmfrac: Simulation and Statistical Analysis of Multifractional Processes

Simulation of fractional Brownian motion

Description

This function simulates a realisation of the fractional Brownian motion over the time interval [t_start,t_end] for a provided Hurst parameter, which has the initial value x_start.

Usage

FBm(H, x_start = 0, t_start = 0, t_end = 1, N = 1000, plot = FALSE)

Arguments

H	Hurst parameter which lies between 0 and 1.
x_start	Value of the process at the initial time point (additive constant mean).
t_start	Initial time point.
t_end	Terminal time point.
N	Number of time steps on the interval [t_start,t_end]. Default set to 1000.
plot	Logical: If TRUE, the realisation of the fractional Brownian motion is plotted in interactive sessions.

Value

A data frame where the first column is t and second column is simulated values of the realisation of fractional Brownian motion with added constant mean.

References

Banna, O., Mishura, Y., Ralchenko, K., & Shklyar, S. (2019). Fractional Brownian motion: Approximations and Projections. John Wiley & Sons. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1002/9781119476771.app3")}.

See Also

FGn, Bm, GHBMP, Bbridge, FBbridge

Examples

FBm(H = 0.5, plot = TRUE)

Rmfrac documentation built on Sept. 10, 2025, 10:31 a.m.