Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1508-50
Keywords
Brownian and fractional Brownian motion process, linear stochastic integral equation, hat functions
First Page
611
Last Page
624
Recommended Citation
HASHEMI, B. H, KHODABIN, M, & MALEKNEJAD, K (2017). Numerical method for solving linear stochasticIto-Volterra integral equations driven by fractional Brownian motion using hat functions. Turkish Journal of Mathematics 41 (3): 611-624. https://doi.org/10.3906/mat-1508-50
