The Sim.DiffProc Package

A.C. Guidoum1 and K. Boukhetala2

GitHub Code Coverge J. Stat. Softw
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Package Overview

The package Sim.DiffProc is an object created in R for symbolic and numerical computations on scalar and multivariate systems of stochastic differential equations. It provides users with a wide range of tools to simulate, estimate, analyze, and visualize the dynamics of these systems in both forms Ito and Stratonovich. The project was officially launched in September 2010 and is under active development by the authors. The current feature set of the package can be split in more main categories: Computing the stochastic integrals of Ito or Stratonovich type. Simulation sde’s and bridge sde’s of Ito or Stratonovich type (1,2 and 3-dim), with different methods. Approximate transition density and random number generators for SDE’s. Density approximation for First-passage-time (f.p.t) in SDE’s (1,2 and 3-dim). Statistical analysis with Parallel Monte-Carlo and moment equations methods of SDE’s (1,2 and 3-dim). Estimate drift and diffusion parameters using pseudo-maximum likelihood estimators of 1-dim SDE’s. Displaying an object inheriting from a class of SDE’s.

The package includes the following categories (where k=1,2,3):

  1. snssdekd() & dsdekd() & rsdekd()- Monte-Carlo Simulation and Analysis of Stochastic Differential Equations.
  2. bridgesdekd() & dsdekd() & rsdekd() - Constructs and Analysis of Bridges Stochastic Differential Equations.
  3. fptsdekd() & dfptsdekd() - Monte-Carlo Simulation and Kernel Density Estimation of First passage time.
  4. MCM.sde() & MEM.sde() - Parallel Monte-Carlo and Moment Equations for SDEs.
  5. TEX.sde() - Converting Sim.DiffProc Objects to LaTeX.
  6. fitsde() - Parametric Estimation of 1-D Stochastic Differential Equation.

Obtaining and installation

As Sim.DiffProc is an R package, it requires R version 4.0.0 or higher to be installed, distributed as open source software under the GPL-2/GPL-3 license. The package is available from CRAN at URL, or from GitHub at URL To download, install and load the current release, just type the code below in your current R session:

## Or 

Documentation and Examples

It is a requirement of the R packaging system that every function and data set in a package has a help page. The Sim.DiffProc package follows this requirement strictly. In addition to the help pages, the package includes vignettes and demonstration scripts. First read the package vignette Then read the reference manual.

browseVignettes(package = "Sim.DiffProc")


demo(package = "Sim.DiffProc")

Collaboration and citation

Obviously, the package leaves many other fields of stochastic modeling with Ito and Stratonovich SDE’s untouched. For this situation to change, we hope that experts in their field will join their efforts to ours and contribute code to the Sim.DiffProc project. The project will continue to grow and improve by the authors to the community of developers and users. If you use Sim.DiffProc please cite the software in publications; use citation() for information on how to cite the software;

citation(package = "Sim.DiffProc")
# To cite package 'Sim.DiffProc' in publications use:

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.

A BibTeX entry for LaTeX users is

    title = {Performing Parallel Monte Carlo and Moment Equations Methods for It\^{o} and Stratonovich 
      Stochastic Differential Systems: {R} Package {Sim.DiffProc}},
    author = {Arsalane Chouaib Guidoum and Kamal Boukhetala},
    journal = {Journal of Statistical Software},
    year = {2020},
    volume = {96},
    number = {2},
    pages = {1--82},
    doi = {10.18637/jss.v096.i02},


Please send comments, error reports, etc. to the author via the addresses email.


  1. 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,

  1. Department of Mathematics and Computer Science, Faculty of Sciences and Technology, University of Tamanghasset, Algeria, E-mail (

  2. Faculty of Mathematics, University of Science and Technology Houari Boumediene, BP 32 El-Alia, U.S.T.H.B, Algeria, E-mail (