rcOU {sde} | R Documentation |
Density, distribution function, quantile function and random generation for the conditional law Xt+Dt|Xt=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 |
This package is a companion to the book Simulation and Inference for Stochastic Differential Equation, Springer, NY.
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))