rsOU: Ornstein-Uhlenbeck or Vasicek process stationary law

In sde: Simulation and Inference for Stochastic Differential Equations

Ornstein-Uhlenbeck or Vasicek process stationary law

Description

Density, distribution function, quantile function, and random generation for the stationary law of the Ornstein-Uhlenbeck process also known as the Vasicek process.

Usage

dsOU(x, theta, log = FALSE)
psOU(x, theta, lower.tail = TRUE, log.p = FALSE) 
qsOU(p, theta, lower.tail = TRUE, log.p = FALSE)
rsOU(n=1, theta)

Arguments

x	vector of quantiles.
p	vector of probabilities.
theta	parameter of the Ornstein-Uhlenbeck process; see details.
n	number of random numbers to generate from the conditional distribution.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x]; otherwise P[X > x].

Details

This function returns quantities related to the stationary law of the process solution of

dX_t = (theta[1]-theta[2]*Xt)*dt + theta[3]*dWt.

Contraints: theta[2]>0, theta[3]>0.

Please note that the process is stationary only if theta[2]>0.

Value

x	a numeric vector

Author(s)

Stefano Maria Iacus

References

Uhlenbeck, G. E., Ornstein, L. S. (1930) On the theory of Brownian motion, Phys. Rev., 36, 823-841.

Vasicek, O. (1977) An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, 5, 177-188.

See Also

rcOU

Examples

rsOU(n=1, theta=c(0,2,1))

sde documentation built on Sept. 9, 2022, 3:07 p.m.