Density, distribution function, quantile function, and random generation for the transition probabilities in the (shifted) Ornstein-Uhlenbeck process given by the stochastic differential equation dX = lambda*(xi-X)*dt + sigma*dB
dOU(x,x0,lambda,xi,sigma,t,log=FALSE)
pOU(x,x0,lambda,xi,sigma,t,log.p=FALSE,lower.tail=TRUE)
qOU(p,x0,lambda,xi,sigma,t,log.p=FALSE,lower.tail=TRUE)
rOU(n,x0,lambda,xi,sigma,t)Arguments
- x, q
Target state, assumed >= 0
- x0
Initial state, assumed > 0
- lambda
Rate parameter, assumed > 0
- xi
Mean parameter, assumed > 0
- sigma
Noise intensity parameters, assumed > 0
- t
Terminal time, assumed > 0 #' @param log,log.p Logical, if TRUE, probabilities/densities are given as log(p). Default is FALSE
- lower.tail
Logical; if TRUE (default) probabilities are P(X<=x); otherise, P(X>x).
- p
Probability, assumed >= 0 and <= 1.
Value
dOU gives the transition probability density, pOU gives the distribution of the transitio probability, qOU gives the quantiles, and rOU samples a random terminal point.
The length of the result is determined by n for rOU, and is the maximum of the lengths of the numerical arguments for the other functions.
