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.

## 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 Data Generator:
`tidy_fft()`

,
`ts_brownian_motion_augment()`

,
`ts_geometric_brownian_motion_augment()`

,
`ts_geometric_brownian_motion()`

,
`ts_random_walk()`

## 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
```