discrete_walk: Discrete Sampled Walk

In RandomWalker: Generate Random Walks Compatible with the 'tidyverse'

Discrete Sampled Walk

Description

The discrete_walk function generates multiple random walks over discrete time periods. Each step in the walk is determined by a probabilistic sample from specified upper and lower bounds. This function is useful for simulating stochastic processes, such as stock price movements or other scenarios where outcomes are determined by a random process.

Usage

discrete_walk(
  .num_walks = 25,
  .n = 100,
  .upper_bound = 1,
  .lower_bound = -1,
  .upper_probability = 0.5,
  .initial_value = 100,
  .dimensions = 1
)

Arguments

.num_walks	Total number of simulations.
.n	Total time of the simulation.
.upper_bound	The upper bound of the random walk.
.lower_bound	The lower bound of the random walk.
.upper_probability	The probability of the upper bound. Default is 0.5. The lower bound is calculated as 1 - .upper_probability.
.initial_value	The initial value of the random walk. Default is 100.
.dimensions	The default is 1. Allowable values are 1, 2 and 3.

Details

The function discrete_walk simulates random walks for a specified number of simulations (.num_walks) over a given total time (.n). Each step in the walk is either the upper bound or the lower bound, determined by a probability (.upper_probability). The initial value of the walk is set by the user (.initial_value), and the cumulative sum, product, minimum, and maximum of the steps are calculated for each walk. The results are returned in a tibble with detailed attributes, including the parameters used for the simulation.

Value

A tibble containing the generated random walks with columns depending on the number of dimensions:

• walk_number: Factor representing the walk number.

• step_number: Step index.

• y: If .dimensions = 1, the value of the walk at each step.

• x, y: If .dimensions = 2, the values of the walk in two dimensions.

• x, y, z: If .dimensions = 3, the values of the walk in three dimensions.

The following are also returned based upon how many dimensions there are and could be any of x, y and or z:

• cum_sum: Cumulative sum of dplyr::all_of(.dimensions).

• cum_prod: Cumulative product of dplyr::all_of(.dimensions).

• cum_min: Cumulative minimum of dplyr::all_of(.dimensions).

• cum_max: Cumulative maximum of dplyr::all_of(.dimensions).

• cum_mean: Cumulative mean of dplyr::all_of(.dimensions).

Author(s)

Steven P. Sanderson II, MPH

See Also

Other Generator Functions: brownian_motion(), geometric_brownian_motion(), random_normal_drift_walk(), random_normal_walk()

Examples

set.seed(123)
discrete_walk()

set.seed(123)
discrete_walk(.dimensions = 3) |>
  head() |>
  t()

RandomWalker documentation built on June 8, 2025, 12:15 p.m.