rcOU: Ornstein-Uhlenbeck or Vasicek process conditional law

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

View source: R/rOU.R

Description

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.

Usage

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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)

Arguments

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].

Details

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.

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

rsOU

Examples

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rcOU(n=1, Dt=0.1, x0=1, theta=c(0,2,1))

Example output

Loading required package: MASS
Loading required package: stats4
Loading required package: fda
Loading required package: splines
Loading required package: Matrix

Attaching package: 'fda'

The following object is masked from 'package:graphics':

    matplot

Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

sde 2.0.15
Companion package to the book
'Simulation and Inference for Stochastic Differential Equations With R Examples'
Iacus, Springer NY, (2008)
To check the errata corrige of the book, type vignette("sde.errata")
[1] 1.026021

sde documentation built on May 31, 2017, 3:58 a.m.