Simulation of Diffusion Processes

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 SDE's. 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.



title: "The Sim.DiffProc Package" author:

  • A.C. Guidoum^[Department of Probabilities & Statistics, Faculty of Mathematics, University of Science and Technology Houari Boumediene, BP 32 El-Alia, U.S.T.H.B, Algeria, E-mail ([email protected])] and K. Boukhetala^[Faculty of Mathematics, University of Science and Technology Houari Boumediene, BP 32 El-Alia, U.S.T.H.B, Algeria, E-mail ([email protected])] output: html_document: keep_md: yes self_contained: no


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CRAN minimal R version


Rdoc


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 2.15.1 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 https://CRAN.R-project.org/package=Sim.DiffProc, or from GitHub at URL https://github.com/acguidoum/Sim.DiffProc. To download, install and load the current release, just type the code below in your current R session:

install.packages("Sim.DiffProc")  ## stable version
install.packages("devtools")
devtools::install_github("acguidoum/Sim.DiffProc")  ## development version
library("Sim.DiffProc")

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")

and

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("Sim.DiffProc")
# To cite package 'Sim.DiffProc' in publications use:
#   Arsalane Chouaib Guidoum and Kamal Boukhetala (2018).
#   Sim.DiffProc: Simulation of Diffusion Processes.R package
#   version 4.2.https://cran.r-project.org/package=Sim.DiffProc
# A BibTeX entry for LaTeX users is
#   @Manual{,
#     title = {Sim.DiffProc: Simulation of Diffusion Processes.},
#     author = {Arsalane Chouaib Guidoum and Kamal Boukhetala},
#     year = {2018},
#     note = {R package version 4.3},
#     url = {https://cran.r-project.org/package=Sim.DiffProc},
#   }

Note

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

References

  1. Guidoum AC, Boukhetala K (2018). Performing Parallel Monte Carlo and Moment Equations Methods for Ito and Stratonovich Stochastic Differential Systems: R Package Sim.DiffProc. Preprint submitted to Journal of Statistical Software.

  2. Guidoum AC, Boukhetala K (2018). Sim.DiffProc: Simulation of Diffusion Processes. R package version 4.3, URL https://cran.r-project.org/package=Sim.DiffProc.

News

Version 3.6: 2016-11-13 o Version 3.5 released. o Minor bug fixes: R (>= 3.3.2).

Version 3.5: 2016-11-10 o Version 3.5 released. o Addition a new functions "dsde" 1,2 and 3-dim, for approximation the conditional density. o Addition a new functions "dfptsde" 1,2 and 3-dim, for approximation the density of first-passage-time. o Addition a new functions "rfptsde" 1,2 and 3-dim, for random generation of first-passage-time.
o Other minor bug fixes: R (>= 3.3.1).

Version 3.4: 2016-10-08 o Version 3.4 released. o Modified function rsde1d, rsde2d and rsde3d. o Modified function fptsde1d, fptsde2d and fptsde3d. o Other minor bug fixes: R (>= 3.3.1).

Version 3.3: 2016-09-21 o Version 3.3 released. o Modified "summary" function for snssde1d, snssde2d and snssde3d classes. o Fixed some bugs in Sim.DiffProc.c o Other minor bug fixes: R (>= 3.3.0).

Version 3.2: 2016-02-09 o Version 3.2 released. o Other minor bug fixes: R (>= 3.2.3).

Version 3.1: 2015-12-31 o Version 3.1 released. o Other minor bug fixes: R (>= 3.2.3).

Version 3.0: 2015-10-30 o Version 3.0 released. o Other minor bug fixes: R (>= 3.2.1).

Version 2.9: 2014-09-10 o Version 2.9 released. o Addition a new argument in bridgesde1d, bridgesde2d and bridgesde3d, possibility of simulating flow paths. o Other minor bug fixes: R (>= 3.0.0).

Version 2.8: 2014-08-18 o Version 2.8 released. o Numerical methods are reprogrammed with C language 'Quick execution time'. o Addition a new argument in snssde2d and snssde3d, possibility of simulating flow paths.
o Addition a new argument in fptsde1d, fptsde2d and fptsde3d functions, first-passage-time with time-dependent boundary.
o Possibility of displays for fptsde2d, fptsde3d, rsde2d and rsde3d functions.
o Manual update. o Many help-file improvements.
o Other minor bug fixes: R (>= 3.0.0).

Version 2.7: 2014-07-13 o Version 2.7 released. o Other minor bug fixes: R (>= 3.0.0).

Version 2.6: 2014-05-04 o Version 2.6 released. o Addition a new type of SDE "Stratonovich" in "snssde1d", "snssde2d" and "snssde3d" functions. o Addition a new numerice methods "Runge-Kutta Order 1 and 2" add in "snssde1d", "snssde2d" and "snssde3d" functions. o Addition a new function "st.int". o Addition a new function "fitsde". o Addition a new function "fptsde" in 1,2 and 3-dim sde. o Addition a new function "rsde" in 1,2 and 3-dim sde. o Manual update. o Many help-file improvements. o Other minor bug fixes: R (>= 2.15.1).

Version 2.5: 2012-06-09 o Version 2.5 released. o Other minor bug fixes: R (>= 2.15.1).

Version 2.2: 2012-02-13 o Version 2.2 released. o Rename the default in read.xlsx, createSheet and removeSheet to sheetName="Sheet1" from "Sheet 1". This makes it consistent with Excel 2007 and 2010 names of an empty workbook.

Version 2.1: 2011-11-18 o Version 2.1 released. o A new function "Appdcon" approximated the evolution conditional law a diffusion process by Euler method, Kessler s'methods and Shoji-Ozaki methods.

Version 2.0: 2011-02-13 o Version 2.0 released.

Version 1.0: 2011-01-04 o Version 1.0 released.

Reference manual

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