Journal ArticleDOI
A collocation technique for solving nonlinear Stochastic Itô-Volterra integral equations
Farshid Mirzaee,Elham Hadadiyan +1 more
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TLDR
A numerical method for solving nonlinear Stochastic Ito-Volterra equations is proposed based on delta function approximations and the properties of DFs and their operational matrix of integration together with the Newton-Cotes nodes are presented.About:
This article is published in Applied Mathematics and Computation.The article was published on 2014-11-15. It has received 28 citations till now. The article focuses on the topics: Collocation method & Nonlinear system.read more
Citations
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Chebyshev cardinal wavelets and their application in solving nonlinear stochastic differential equations with fractional Brownian motion
TL;DR: A new computational method is proposed to solve a class of nonlinear stochastic differential equations (SDEs) driven by fractional Brownian motion, based on a new class of orthogonal wavelets, namely the Chebyshev cardinal wavelets.
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Euler polynomial solutions of nonlinear stochastic Itô–Volterra integral equations
TL;DR: A practical matrix method based on operational matrices of integration and collocation points is presented to find the approximate solution of nonlinear stochastic Ito–Volterra integral equations and an upper error bound is provided under mild conditions.
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Chebyshev cardinal wavelets for nonlinear stochastic differential equations driven with variable-order fractional Brownian motion
TL;DR: In this paper, a computational approach based on the Chebyshev cardinal wavelets for a novel class of nonlinear stochastic differential equations characterized by the presence of variable-order fractional Brownian motion was proposed.
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Strong superconvergence of the EulerMaruyama method for linear stochastic Volterra integral equations
TL;DR: The EulerMaruyama method is presented for linear stochastic Volterra integral equations, then the strong convergence property is analyzed for convolution kernels and general kernels, respectively, and the strong superconvergence order of 1 is obtained.
Journal ArticleDOI
A computational method for solving nonlinear stochastic Volterra integral equations
Farshid Mirzaee,Afsun Hamzeh +1 more
TL;DR: By using new adjustment of hat basis functions and their stochastic operational matrix of integration, the NSIVIE is reduced to a nonlinear system of algebraic equations.
References
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Book
Numerical Solution of Stochastic Differential Equations
Peter E. Kloeden,Eckhard Platen +1 more
TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.
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Backward stochastic volterra integral equations and some related problems
TL;DR: In this article, a duality principle between linear stochastic Volterra integral equations and (forward)-stochastic VOLTERRA integral equations is presented, and a comparison theorem is proved for the adapted solutions of BSVIEs.
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Euler schemes and large deviations for stochastic Volterra equations with singular kernels
TL;DR: In this article, an Euler type approximation is constructed for stochastic Volterra equation with singular kernels, which provides an algorithm for numerical calculation, and the large deviation estimates of small perturbation to equations of this type are obtained.
Journal ArticleDOI
Numerical solution of a class of two-dimensional nonlinear Volterra integral equations using Legendre polynomials
TL;DR: The operational matrices of integration and product together with the collocation points are utilized to reduce the solution of the integral equation to the Solution of a system of nonlinear algebraic equations.
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Volterra Equations Driven by Semimartingales
TL;DR: In this article, the existence and uniqueness of solutions for stochastic Volterra integral equations driven by right continuous semimartingales is established, which resolves a conjecture of M. Berger and V. Mizel.