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

Authors

BENTOL HODA HASHEMI
MORTEZA KHODABIN
KHOSROW MALEKNEJAD

DOI

10.3906/mat-1508-50

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

First Page

611

Last Page

624

Recommended Citation

HASHEMI, BENTOL HODA; KHODABIN, MORTEZA; and MALEKNEJAD, KHOSROW (2017) "Numerical method for solving linear stochasticIto-Volterra integral equations driven by fractional Brownian motion using hat functions," Turkish Journal of Mathematics: Vol. 41: No. 3, Article 13. https://doi.org/10.3906/mat-1508-50
Available at: https://journals.tubitak.gov.tr/math/vol41/iss3/13