Create a Brownian Motion Tibble
Usage
brownian_motion(
.num_walks = 25,
.n = 100,
.delta_time = 1,
.initial_value = 0,
.return_tibble = TRUE
)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:
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.
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()
#> # A tibble: 2,525 × 6
#> walk_number x y cum_min cum_max cum_mean
#> <fct> <int> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1 0 0 0 0
#> 2 1 2 -0.560 -0.560 0 -0.280
#> 3 1 3 -0.791 -0.791 0 -0.450
#> 4 1 4 0.768 -0.791 0.768 -0.146
#> 5 1 5 0.839 -0.791 0.839 0.0511
#> 6 1 6 0.968 -0.791 0.968 0.204
#> 7 1 7 2.68 -0.791 2.68 0.558
#> 8 1 8 3.14 -0.791 3.14 0.881
#> 9 1 9 1.88 -0.791 3.14 0.992
#> 10 1 10 1.19 -0.791 3.14 1.01
#> # ℹ 2,515 more rows
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")
