rsOU: Ornstein-Uhlenbeck or Vasicek process stationary law

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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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

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


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