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

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 |

`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.

1 |

```
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.

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