BMRW: Creating Brownian Motion Model (by a Random Walk)
Description
Simulation of the brownian motion model by a Random Walk.
Usage
BMRW(N, t0, T, C, output = FALSE)
Arguments
N
size of process.
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
One characterization of the Brownian motion says that it can be seen as the limit of a random walk in the following sense.
Given a sequence of independent and identically distributed random variables X1, X2, . . . , Xn, taking only two values +1 and -1 with equal probability and considering the partial sum, Sn = X1+ X2+ . . . + Xn. then, as n --> lnf,P(Sn/sqrt(N) < x) = P( W(t) < x).
Where [x] is the integer part of the real number x. Please note that this result is a refinement of the central limit theorem that, in our case, asserts that Sn/sqrt(n) ~~> N(0,1).
See Also
BMN simulation brownian motion by the normal distribution, BMNF simulation flow 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.