Monte Carlo-type simulation for solving stochastic ordinary differential equations
type: Item
instance of: scholarly article
title: Monte Carlo-type simulation for solving stochastic ordinary differential equations
zbMATH Open document ID: 0597.65068
DOI: 10.1016/0378-4754(87)90134-0
author: Renato Spigler
published in: Mathematics and Computers in Simulation
publication date: 1987-01-01T00:00:00Z
review text: We outline a method for solving numerically initial-value and boundary- value problems for ordinary differential equations whose coefficients and/or initial and boundary data are random quantities. The method consists of simulating on the computer several realizations of the stochastic processes that appear in the coefficients of the equations and similarly for the data. Such a simulation is based upon generating suitable sequences of random numbers, for which reason the method can be thought of as a Monte Carlo method. We then solve ''pathwise'' the equation and finally compute the quantities of interest such as expected values, moments, etc. over such realizations. The numerical error can also be estimated. The method is very simple but quite general, moreover it respects the correct probabilistic structure of the problem and is trivially suited to parallel implementation.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65C10
zbMATH DE Number: 3963124
zbMATH Keywords: stochastic ordinary differential equations
zbMATH Keywords: stochastic processes
zbMATH Keywords: parallel implementation
zbMATH Keywords: random numbers
zbMATH Keywords: Monte Carlo method
MaRDI profile type: Publication
full work available at URL: 0378-4754(87)90134-0
OpenAlex ID: W1980503817
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description: scientific article; zbMATH DE number 3963124