Density, distribution function, quantile function, and random generation for the stationary law of the Ornstein-Uhlenbeck process also known as the Vasicek process.

1 2 3 4 |

`x` |
vector of quantiles. |

`p` |
vector of probabilities. |

`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 |

`lower.tail` |
logical; if TRUE (default), probabilities are |

This function returns quantities related to the stationary law of the process solution of

*dX_t = (theta[1]-theta[2]*Xt)*dt + theta[3]*dWt.*

Contraints: *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`

1 |

Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.

All documentation is copyright its authors; we didn't write any of that.