Performing Parallel Monte Carlo and Moment Equations Methods for Itô and Stratonovich Stochastic Differential Systems: R Package Sim.DiffProc
Dublin Core
Title
Performing Parallel Monte Carlo and Moment Equations Methods for Itô and Stratonovich Stochastic Differential Systems: R Package Sim.DiffProc
Subject
stochastic differential equation, stochastic calculus, moment equations, Monte
Carlo simulation, parallel computing, statistical sampling, statistical analysis, nonparametric,
transition density, reproducible research, LATEX, R.
Carlo simulation, parallel computing, statistical sampling, statistical analysis, nonparametric,
transition density, reproducible research, LATEX, R.
Description
We introduce Sim.DiffProc, an R package for symbolic and numerical computations
on scalar and multivariate systems of stochastic differential equations (SDEs). It provides
users with a wide range of tools to simulate, estimate, analyze, and visualize the dynamics
of these systems in both forms, Itô and Stratonovich. One of Sim.DiffProc key features
is to implement the Monte Carlo method for the iterative evaluation and approximation
of an interesting quantity at a fixed time on SDEs with parallel computing, on multiple
processors on a single machine or a cluster of computers, which is an important tool to
improve capacity and speed-up calculations. We also provide an easy-to-use interface for
symbolic calculation and numerical approximation of the first and central second-order
moments of SDEs (i.e., mean, variance and covariance), by solving a system of ordinary
differential equations, which yields insights into the dynamics of stochastic systems. The
final result object of Monte Carlo and moment equations can be derived and presented in
terms of LATEX math expressions and visualized in terms of LATEX tables.
Furthermore, we illustrate various features of the package by proposing a general
bivariate nonlinear dynamic system of Haken-Zwanzig, driven by additive, linear and
nonlinear multiplicative noises. In addition, we consider the particular case of a scalar
SDE driven by three independent Wiener processes. The Monte Carlo simulation thereof
is obtained through a transformation to a system of three equations. We also study some
important applications of SDEs in different fields
on scalar and multivariate systems of stochastic differential equations (SDEs). It provides
users with a wide range of tools to simulate, estimate, analyze, and visualize the dynamics
of these systems in both forms, Itô and Stratonovich. One of Sim.DiffProc key features
is to implement the Monte Carlo method for the iterative evaluation and approximation
of an interesting quantity at a fixed time on SDEs with parallel computing, on multiple
processors on a single machine or a cluster of computers, which is an important tool to
improve capacity and speed-up calculations. We also provide an easy-to-use interface for
symbolic calculation and numerical approximation of the first and central second-order
moments of SDEs (i.e., mean, variance and covariance), by solving a system of ordinary
differential equations, which yields insights into the dynamics of stochastic systems. The
final result object of Monte Carlo and moment equations can be derived and presented in
terms of LATEX math expressions and visualized in terms of LATEX tables.
Furthermore, we illustrate various features of the package by proposing a general
bivariate nonlinear dynamic system of Haken-Zwanzig, driven by additive, linear and
nonlinear multiplicative noises. In addition, we consider the particular case of a scalar
SDE driven by three independent Wiener processes. The Monte Carlo simulation thereof
is obtained through a transformation to a system of three equations. We also study some
important applications of SDEs in different fields
Creator
Arsalane Chouaib Guidoum
Source
https://www.jstatsoft.org/article/view/v096i02
Publisher
University of Science and Technology
Houari Boumediene
Houari Boumediene
Date
November 2020
Contributor
Fajar bagus W
Format
PDF
Language
Inggris
Type
Text
Files
Collection
Citation
Arsalane Chouaib Guidoum, “Performing Parallel Monte Carlo and Moment Equations Methods for Itô and Stratonovich Stochastic Differential Systems: R Package Sim.DiffProc,” Repository Horizon University Indonesia, accessed April 4, 2025, https://repository.horizon.ac.id/items/show/8168.