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”).
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
to obtain the approximation of the f.p.t. density.
In the general case (conditioned and unconditioned f.p.t. problems) the function
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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