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 the Vasicek process.
1 2 3 4 |
x |
vector of quantiles. |
p |
vector of probabilities. |
Dt |
lag or time. |
x0 |
the value of the process at time |
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 |
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.
rsOU
1 |
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