Generation of a random trajectory of an OU process starting from a given initial state

Generates a trajectory xt given initial state z0 according to an Ornstein-Uhlenbeck process.

rTrajectoryOU(z0, t, alpha, theta, sigma, steps = 1)

Arguments

z0	Numeric value, initial state.
t	Numeric value or vector of size steps, denoting the time-step(s).
alpha, theta, sigma	Numeric values, parameters of the OU process.
steps	Integer, number of steps.

Value

A numeric vector of length steps containing the generated values at times 0+t, 0+2t, ..., 0+steps*t.

Examples

z0 <- 0
nSteps <- 100
t <- 0.01
trajectory <- rTrajectoryOU(z0, t, 2, 2, 1, steps = nSteps)
plot(trajectory, type = 'l')