BMNF: Creating Flow of Brownian Motion (by the Normal Distribution)
Description
Simulation flow of the brownian motion model by the normal distribution.
Usage
BMNF(N, M, t0, T, C, output = FALSE)
Arguments
N
size of process.
M
number of trajectories.
t0
initial time.
T
final time.
C
constant positive (if C = 1 it is standard brownian motion).
output
if output = TRUE write a output to an Excel (.csv).
Value
data.frame(time,x) and plot of process.
Details
Given a fixed time increment dt = (T-t0)/N, one can easily simulate a flow of the Wiener process in the time interval [t0,T]. Indeed, for W(dt) it holds true that W(dt) = W(dt) - W(0) ~> N(0,dt) ~> sqrt(dt) * N(0,1), N(0,1) normal distribution.
See Also
BMRW simulation brownian motion by a random walk, BMN simulation of brownian motion by the normal distribution, BMRWF simulation flow of brownian motion by a random walk, BB Simulation of brownian bridge model, GBM simulation geometric brownian motion Model.