A efficient computational method for solving stochastic itô-volterra integral equations

In this paper, a new stochastic operational matrix for the Legendre wavelets is presented and a general procedure for forming this matrix is given. A computational method based on this stochastic operational matrix is proposed for solving stochastic Itô-Voltera integral equations. Convergence and error analysis of the Legendre wavelets basis are investigated. To reveal the accuracy and efficiency of the proposed method some numerical examples are included.Publisher's Versio

Modified Block Pulse Functions for Numerical Solution of Stochastic Volterra Integral Equations

We present a new technique for solving numerically stochastic Volterra integral equation based on modified block pulse functions. It declares that the rate of convergence of the presented method is faster than the method based on block pulse functions. Efficiency of this method and good degree of accuracy are confirmed by a numerical example

Numerical Implementation of Stochastic Operational Matrix Driven by a Fractional Brownian Motion for Solving a Stochastic Differential Equation

An efficient method to determine a numerical solution of a stochastic differential equation (SDE) driven by fractional Brownian motion (FBM) with Hurst parameter H∈(1/2,1) and n independent one-dimensional standard Brownian motion (SBM) is proposed. The method is stated via a stochastic operational matrix based on the block pulse functions (BPFs). With using this approach, the SDE is reduced to a stochastic linear system of m equations and m unknowns. Then, the error analysis is demonstrated by some theorems and defnitions. Finally, the numerical examples demonstrate applicability and accuracy of this method