Numerical method for solving linear stochastic Ito-Volterra integral equations driven by fractional Brownian motion using hat functions

Authors : Bentol Hoda Hashemi, Morteza Khodabin, Khosrow Maleknejad

Pages : 611-624

View : 12 | Download : 6

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :In this paper, we present a numerical method to approximate the solution of linear stochastic Ito-Volterra integral equations driven by fractional Brownian motion with Hurst parameter $ H \in (0,1)$ based on a stochastic operational matrix of integration for generalized hat basis functions. We obtain a linear system of algebraic equations with a lower triangular coefficients matrix from the linear stochastic integral equation, and by solving it we get an approximation solution with accuracy of order $ \emph{O}(h^2)$. This numerical method shows that results are more accurate than the block pulse functions method where the rate of convergence is $ \emph{O}(h)$. Finally, we investigate error analysis and with some examples indicate the efficiency of the method.
Keywords : Brownian and fractional Brownian motion process, linear stochastic integral equation, hat functions