Create a Brownian Motion Tibble

## Usage

ts_brownian_motion(
.time = 100,
.num_sims = 10,
.delta_time = 1,
.initial_value = 0,
.return_tibble = TRUE
)

## Arguments

.time

Total time of the simulation.

.num_sims

Total number of simulations.

.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.

A tibble/matrix

## 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.

Other Data Generator: tidy_fft(), ts_brownian_motion_augment(), ts_geometric_brownian_motion_augment(), ts_geometric_brownian_motion(), ts_random_walk()

## Author

Steven P. Sanderson II, MPH

## Examples

ts_brownian_motion()
#> # A tibble: 1,010 × 3
#>    sim_number        t     y
#>    <fct>         <int> <dbl>
#>  1 sim_number 1      1     0
#>  2 sim_number 2      1     0
#>  3 sim_number 3      1     0
#>  4 sim_number 4      1     0
#>  5 sim_number 5      1     0
#>  6 sim_number 6      1     0
#>  7 sim_number 7      1     0
#>  8 sim_number 8      1     0
#>  9 sim_number 9      1     0
#> 10 sim_number 10     1     0
#> # ℹ 1,000 more rows