Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations

The purpose of this paper is to present a simple numerical technique for approximating the solutions of stochastic Volterra integral equations. The proposed method depends on the Picard iteration and uses a suitable quadrature rule. Error estimates and associated theorems have been proved for this p...

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Vydáno v:Numerical algorithms Ročník 99; číslo 2; s. 809 - 835
Hlavní autor: Zeghdane, Rebiha
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.06.2025
Springer Nature B.V
Témata:
Algebra
Algorithms
Approximation
Banach spaces
Computer Science
Integral equations
Iterative methods
Numeric Computing
Numerical Analysis
Original Paper
Picard iterations
Quadratures
Random variables
Stochastic models
Theory of Computation
Volterra integral equations
Itô integral
Picard iteration
Quadrature formula
Numerical solution
Stochastic differential equation
ISSN:1017-1398, 1572-9265
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Shrnutí:The purpose of this paper is to present a simple numerical technique for approximating the solutions of stochastic Volterra integral equations. The proposed method depends on the Picard iteration and uses a suitable quadrature rule. Error estimates and associated theorems have been proved for this proposed technique. Some test examples have been studied to verify the applicability and accuracy of the proposed technique.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01898-6