Second kind Chebyshev wavelet Galerkin method for stochastic Itô-Volterra integral equations
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.
stochastic Itô-Volterra integral equations
scientific article; zbMATH DE number 6661791
scientific article