rsOU {sde}R Documentation

Ornstein-Uhlenbeck or Vasicek process stationary law

Description

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

Note

This package is a companion to the book `Simulation and Inference for Stochastic Differential Equation, Springer, NY.

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))

[Package sde version 1.9.5 Index]