simulate (un)biased random walk

Simulates a (continuous time) random walk as a Brownian drift. For mu = 0 the random walk is unbiased, otherwise it is biased.

Usage

random_walk(t, sigma = 1, mu = 0, y0 = 0)

Arguments

t

numeric vector with strictly increasing elements, can be heterodistant. Times at which the random walk is evaluated

sigma

positive number, variance parameter

mu

number, directionality parameter

y0

number, starting value (value of the random walk at the first entry of t)

Value

A list with elements t and y. t is a duplicate of the input parameter and is the times at which the random walk is evaluated. y are the values of the random walk at said times. Output list is of S3 class timelist (inherits from list) and can thus be plotted directly using plot, see ?admtools::plot.timelist

See also

• stasis() and ornstein_uhlenbeck() to simulate other modes of evolution

• random_walk_sl() to simulate random walk on specimen level - for usage in conjunction with the paleoTS package

Examples

library("admtools") # required for plotting of results
t = seq(0, 1, by = 0.01)
l = random_walk(t, sigma = 3) # high variability, no direction
plot(l, type = "l")
l2 = random_walk(t, mu = 1) # low variabliity, increasing trend
lines(l2$t, l2$y, col = "red")