Sim.DiffProc-package {Sim.DiffProc}R Documentation

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 acguidoum@univ-tam.dz and K. Boukhetala kboukhetala@usthb.dz.
Please send comments, error reports, etc. to the author via the addresses email.

References

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Aytug H., G. J. Koehler (2000). New stopping criterion for genetic algorithms. European Journal of Operational Research, 126, 662–674.

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.

Ding, M. and G. Rangarajan. (2004). First Passage Time Problem: A Fokker-Planck Approach. New Directions in Statistical Physics. ed by L. T. Wille. Springer. 31–46.

Ait-Sahalia, Y. (1999). Transition densities for interest rate and other nonlinear diffusions. The Journal of Finance, 54, 1361–1395.

Ait-Sahalia, Y. (2002). Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach. Econometrica. 70, 223–262.

Roman, R.P., Serrano, J. J., Torres, F. (2008). First-passage-time location function: Application to determine first-passage-time densities in diffusion processes. Computational Statistics and Data Analysis. 52, 4132–4146.

Roman, R.P., Serrano, J. J., Torres, F. (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.

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Iacus, S.M. (2014). sde: Simulation and Inference for Stochastic Differential Equations. R package version 2.0.13.

Brouste, A. et al. (2014). The yuima Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations. Journal of Statistical Software, 57(4).

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Kloeden, P.E, and Platen, E. (1991a). Relations between multiple Itô and stratonovich integrals. Stochastic Analysis and Applications, 9(3), 311–321.

Kloeden, P.E, and Platen, E. (1991b). Stratonovich and Itô stochastic taylor expansions. Mathematische Nachrichten, 151, 33–50.

Kloeden, P.E, and Platen, E. (1995). Numerical Solution of Stochastic Differential Equations. Springer-Verlag, New York.

Oksendal, B. (2000). Stochastic Differential Equations: An Introduction with Applications. 5th edn. Springer-Verlag, Berlin.

B.L.S. Prakasa Rao. (1999). Statistical Inference for Diffusion Type Processes. Arnold, London and Oxford University press, New York.

Kutoyants, Y.A. (2004). Statistical Inference for Ergodic Diffusion Processes. Springer, London.

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

Sorensen, H. (2002). Estimation of diffusion parameters for discretely observed diffusion processes. Bernoulli, 8, 491–508.

Sorensen, H. (2004). Parametric inference for diffusion processes observed at discrete points in time: a survey. International Statistical Review, 72, 337–354.

Platen, E. (1980). Weak convergence of approximations of Itô integral equations. Z Angew Math Mech. 60, 609–614.

Platen, E. and Bruti-Liberati, N. (2010). Numerical Solution of Stochastic Differential Equations with Jumps in Finance. Springer-Verlag, New York.

Itô, Y, and Mitsui, T. (1993). Simulation of Stochastic Differential Equations. The Annals of the Institute of Statistical Mathematics, 3, 419–432.

Risken, H. (2001). The Fokker Planck Equation : Methods of Solutions and Applications. 2nd edition, Springer Series in Synergetics.

Dacunha, D.C. and Florens, D.Z. (1986). Estimation of the Coefficients of a Diffusion from Discrete Observations. Stochastics. 19, 263–284.

Dohnal, G. (1987). On estimating the diffusion coefficient. J. Appl.Prob., 24, 105–114.

Genon, V.C. (1990). Maximum constrast estimation for diffusion processes from discrete observation. Statistics, 21, 99–116.

Protter, P. (2005). Stochastic Integration and Differential Equations. 2nd edn. Springer-Verlag, New York.

Bladt, M. and Sorensen, M. (2007). Simple simulation of diffusion bridges with application to likelihood inference for diffusions. Working Paper, University of Copenhagen.

Ozaki, T. (1992). A bridge between nonlinear time series models and nonlinear stochastic dynamical systems: A local linearization approach. Statistica Sinica, 2, 25-83.

Shoji, L., Ozaki, T. (1998). Estimation for nonlinear stochastic differential equations by a local linearization method. Stochastic Analysis and Applications, 16, 733-752.

Nicolau, J. (2004). Introduction to the estimation of stochastic differential equations based on discrete observations. Autumn School and International Conference, Stochastic Finance.

F C Klebaner, F.C. (2005). Introduction to stochastic calculus with application. 2nd edn. Imperial College Press (ICP).

Henderson, D. and Plaschko, P. (2006). Stochastic differential equations in science and engineering. World Scientific.

See Also

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

[Package Sim.DiffProc version 4.9 Index]