rcOU {sde} | R Documentation |
Density, distribution function, quantile function and
random generation for the conditional law X(t+Dt) | X(t)=x0
of the Ornstein-Uhlenbeck process
also known as Vasicek process
dcOU(x, Dt, x0, theta, log = FALSE) pcOU(x, Dt, x0, theta, lower.tail = TRUE, log.p = FALSE) qcOU(p, Dt, x0, theta, lower.tail = TRUE, log.p = FALSE) rcOU(n=1, Dt, x0, theta)
x |
vector of quantiles. |
p |
vector of probabilities. |
Dt |
lag or time. |
x0 |
the value of the process at time t . See details. |
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] . |
This function returns quantities related to the conditional law
of the process solution of
dX_t = (theta[1] - theta[2]*Xt)*dt + theta[3]*dWt
.
Constraints: theta[2]>0, theta[3]>0
.
Please note that the process is stationary only if theta[2]>0
.
x |
a numeric vector |
Stefano Maria Iacus
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.
rcOU(n=1, Dt=0.1, x0=1, theta=c(0,2,1))