Description Details Author(s) References

Efficient approximation of first-passage-time (f.p.t.) densities for diffusion processes based on the First-Passage-Time Location (FPTL) function.

For a complete list of functions, use library(help=“fptdApprox”).

Package: | fptdApprox |

Type: | Package |

Version: | 2.1 |

Date: | 2015-08-24 |

License: | GPL-2 |

LazyLoad: | yes |

The fptdApprox package allows to approximate efficiently the f.p.t. density for a diffusion process through a continuous time-dependent boundary in the cases of conditioned and unconditioned f.p.t. problems.

For an unconditioned f.p.t. problem, a step by step study can be performed.
First, the diffusion process under consideration must be defined by using the function
`diffproc`

. Then, the `FPTL`

function will be used to calculate the FPTL function for the specified
process and boundary. The information provided by the function is then extracted by the method `summary.fptl`

and used to find the range of
variation of the f.p.t. variable. Finally, such information is used by the function `Approx.cfpt.density`

to obtain the approximation of the f.p.t. density.

In the general case (conditioned and unconditioned f.p.t. problems) the function `Approx.fpt.density`

allows to obtain directly the approximate f.p.t. density.

Patricia Román-Román, Juan J. Serrano-Pérez and Francisco Torres-Ruiz.

Maintainer: Juan J. Serrano-Pérez, [email protected]

Buonocore, A., Nobile, A.G. and Ricciardi, L.M. (1987) A new integral equation for the evaluation of
first-passage-time probability densities. *Adv. Appl. Probab.*, **19**, 784–800.

Román, P., Serrano, J. J., Torres, F. (2008) First-passage-time location function: Application to determine
first-passage-time densities in diffusion processes. *Comput. Stat. Data Anal.*, **52**, 4132–4146.

P. Román-Román, J.J. Serrano-Pérez, F. Torres-Ruiz. (2012) An R package for an efficient approximation of first-passage-time densities for diffusion processes based on the FPTL function. *Applied Mathematics and Computation*, **218**, 8408–8428.

P. Román-Román, J.J. Serrano-Pérez, F. Torres-Ruiz. (2014) More general problems on first-passage times for diffusion processes: A new version of the fptdApprox R package. *Applied Mathematics and Computation*, **244**, 432–446.

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