Sim.DiffProc-package: Simulation of Diffusion Processes

In Sim.DiffProc: Simulation of Diffusion Processes

Simulation of Diffusion Processes

Description

It provides users with a wide range of tools to simulate, estimate, analyze, and visualize the dynamics of stochastic differential systems in both forms Ito and Stratonovich. Statistical analysis with parallel Monte Carlo and moment equations methods of SDEs <doi:10.18637/jss.v096.i02>. Enabled many searchers in different domains to use these equations to modeling practical problems in financial and actuarial modeling and other areas of application, e.g., modeling and simulate of first passage time problem in shallow water using the attractive center (Boukhetala K, 1996) ISBN:1-56252-342-2.

Details

Package:	Sim.DiffProc
Type:	Package
Version:	4.9
Date:	2024-03-06
License:	GPL (>= 2)
Depends:	R (>= 4.0.0)
Imports:	Deriv (>= 3.8.0), MASS (>= 7.3-30), parallel
Suggests:	deSolve (>= 1.11), knitr (>= 1.10), rgl (>= 0.93.991), rmarkdown (>= 0.8), scatterplot3d (>= 0.3-36), sm (>= 2.2-5.3)
Classification/MSC:	37H10, 37M10, 60H05, 60H10, 60H35, 60J60, 65C05, 68N15, 68Q10

There are main types of functions in this package:

1. Simulation of solution to 1,2 and 3-dim stochastic differential equations of Itô and Stratonovich types, with different methods.

2. Simulation of solution to 1,2 and 3-dim diffusion bridge of Itô and Stratonovich types, with different methods.

3. Simulation the first-passage-time (f.p.t) in 1,2 and 3-dim sde of Itô and Stratonovich types.

4. Calculate symbolic ODE's of moment equations (means and variances-covariance) for 1,2 and 3-dim SDE's.

5. Monte-Carlo replicates of a statistic applied to 1,2 and 3-dim SDE's at any time t.

6. Computing the basic statistics (mean, var, median, ...) of the processes at any time t using the Monte Carlo method.

7. Random number generators (RN's) to generate 1,2 and 3-dim sde of Itô and Stratonovich types.

8. Approximate the transition density 1,2 and 3-dim of the processes at any time t.

9. Approximate the density of first-passage-time in 1,2 and 3-dim SDE's.

10. Computing the Itô and Stratonovich stochastic integrals.

11. Estimate drift and diffusion parameters by the method of maximum pseudo-likelihood of the one-dim stochastic differential equation.

12. Converting Sim.DiffProc objects to LaTeX.

13. Displaying an object inheriting from class "sde" (1,2 and 3 dim).

For more examples see demo(Sim.DiffProc), and for an overview of this package, see browseVignettes('Sim.DiffProc') for more informations.

Requirements

R version >= 4.0.0

Citation

Guidoum AC, Boukhetala K (2020). "Performing Parallel Monte Carlo and Moment Equations Methods for Itô and Stratonovich Stochastic Differential Systems: R Package Sim.DiffProc". Journal of Statistical Software, 96(2), 1–82. doi:10.18637/jss.v096.i02

Licence

This package and its documentation are usable under the terms of the "GNU General Public License", a copy of which is distributed with the package.

Author(s)

A.C. Guidoum [e-mail] and K. Boukhetala [e-mail].
Please send comments, error reports, etc. to the author via the addresses email.

References

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Boukhetala, K. (1994). Simulation study of a dispersion about an attractive centre. In proceedings of 11th Symposium Computational Statistics, edited by R.Dutter and W.Grossman, Wien , Austria, 128–130.

Boukhetala, K. (1996). Modelling and simulation of a dispersion pollutant with attractive centre. ed by Computational Mechanics Publications, Southampton ,U.K and Computational Mechanics Inc, Boston, USA, 245–252.

Boukhetala, K. (1998a). Estimation of the first passage time distribution for a simulated diffusion process. Maghreb Math.Rev, 7(1), 1–25.

Boukhetala, K. (1998b). Kernel density of the exit time in a simulated diffusion. les Annales Maghrebines De L ingenieur, 12, 587–589.

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Sorensen, H. (2000). Inference for Diffusion Processes and Stochastic Volatility Models. Ph.D. thesis, Department of Mathematical Sciences, University of Copenhagen.

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See Also

sde, yumia, DiffusionRgqd, DiffusionRjgqd, DiffusionRimp, QPot, diffeqr, fptdApprox.

Sim.DiffProc documentation built on May 29, 2024, 8:09 a.m.