brownian_motion {RandomWalker} | R Documentation |
Brownian Motion
Description
Create a Brownian Motion Tibble
Usage
brownian_motion(
.num_walks = 25,
.n = 100,
.delta_time = 1,
.initial_value = 0,
.return_tibble = TRUE
)
Arguments
.num_walks |
Total number of simulations. |
.n |
Total time of the simulation. |
.delta_time |
Time step size. |
.initial_value |
Integer representing the initial value. |
.return_tibble |
The default is TRUE. If set to FALSE then an object of class matrix will be returned. |
Details
Brownian Motion, also known as the Wiener process, is a continuous-time random process that describes the random movement of particles suspended in a fluid. It is named after the physicist Robert Brown, who first described the phenomenon in 1827.
The equation for Brownian Motion can be represented as:
W(t) = W(0) + sqrt(t) * Z
Where W(t) is the Brownian motion at time t, W(0) is the initial value of the Brownian motion, sqrt(t) is the square root of time, and Z is a standard normal random variable.
Brownian Motion has numerous applications, including modeling stock prices in financial markets, modeling particle movement in fluids, and modeling random walk processes in general. It is a useful tool in probability theory and statistical analysis.
Value
A tibble/matrix
Author(s)
Steven P. Sanderson II, MPH
See Also
Other Generator Functions:
discrete_walk()
,
geometric_brownian_motion()
,
random_normal_drift_walk()
,
random_normal_walk()
Examples
library(ggplot2)
set.seed(123)
brownian_motion()
set.seed(123)
brownian_motion() |>
ggplot(aes(x = x, y = y, group = walk_number, color = walk_number)) +
geom_line() +
labs(title = "Brownian Motion", x = "Time", y = "Value") +
theme_minimal() +
theme(legend.position = "none")