sdetorus (version 0.1.10)

rTrajOu: Simulation of trajectories for the univariate OU diffusion

Description

Simulation of trajectories of the univariate Ornstein--Uhlenbeck (OU) diffusion $$dX_t=\alpha(\mu - X_t)dt+\sigma dW_t, X_0=x_0$$ using the exact transition probability density.

Usage

rTrajOu(x0, alpha, mu, sigma, N = 100, delta = 0.001)

Value

A vector of length N + 1 containing x0 in the first entry and the exact discretized trajectory on the remaining elements.

Arguments

x0

initial point.

alpha

strength of the drift.

mu

unconditional mean of the diffusion.

sigma

diffusion coefficient.

N

number of discretization steps in the resulting trajectory.

delta

time discretization step.

Details

The law of the discretized trajectory is a multivariate normal with mean meantOu and covariance matrix covstOu. See rTrajMou for the multivariate case (less efficient for dimension one).

Examples

isRStudio <- identical(.Platform$GUI, "RStudio")
if (isRStudio) {
  manipulate::manipulate({
   set.seed(345678);
   plot(seq(0, N * delta, by = delta), rTrajOu(x0 = 0, alpha = alpha, mu = 0,
        sigma = sigma, N = N, delta = delta), ylim = c(-4, 4), type = "l",
        ylab = expression(X[t]), xlab = "t")
   }, delta = manipulate::slider(0.01, 5.01, step = 0.1),
   N = manipulate::slider(10, 500, step = 10, initial = 200),
   alpha = manipulate::slider(0.01, 5, step = 0.1, initial = 1),
   sigma = manipulate::slider(0.01, 5, step = 0.1, initial = 1))
}