Ornstein-Uhlenbeck process

Sampling of paths of the Ornstein-Uhlenbeck process.

Usage

r.ou(
  n,
  t = seq(0, 1, len = 201),
  mu = 0,
  alpha = 1,
  sigma = 1,
  x0 = rnorm(n, mean = mu, sd = sigma/sqrt(2 * alpha))
)

Arguments

n

number of curves.

t

discretization points.

mu

mean of the process.

alpha

strength of the drift.

sigma

diffusion coefficient.

x0

a number or a vector of length n giving the initial value(s) of the Ornstein-Uhlenbeck process. By default, n points are sampled from the stationary distribution.

Value

Functional sample, an fdata object of length n.

Author

Eduardo Garcia-Portugues (edgarcia@est-econ.uc3m.es).

Examples

plot(r.ou(n = 100))

plot(r.ou(n = 100, alpha = 2, sigma = 4, x0 = 1:100))