Second kind Chebyshev wavelet Galerkin method for stochastic Itô-Volterra integral equations. (English) Zbl 1359.65015

Using a stochastic operational matrix for the second kind Chebyshev wavelets used as a basis, a Galerkin approximation scheme is devised to obtain numerical approximations for the solution of an Itô stochastic Volterra integral equation of the form \[ X(t)= f(t)+ \int^t_0 \alpha(s, X(s))\,ds + \int^t_0 \sigma(s,X(s))\,dB(s),\quad t\in[0,T), \] where \(B(t)\) is a Brownian motion process. \(L^2\) convergence of the approximate solutions to the exact solution is proved. For three examples numerical results from this method are compared with the exact solution and with results from other numerical methods to illustrate the accuracy and efficiency of this method.


65C30 Numerical solutions to stochastic differential and integral equations
65T60 Numerical methods for wavelets
60H20 Stochastic integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
45R05 Random integral equations
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