Numerical Solution of Nonlinear Stochastic Itô–Volterra Integral Equations Driven by Fractional Brownian Motion Using Block Pulse Functions
Keyword(s):
This paper presents a valid numerical method to solve nonlinear stochastic Itô–Volterra integral equations (SIVIEs) driven by fractional Brownian motion (FBM) with Hurst parameter H ∈ 1 / 2 , 1 . On the basis of FBM and block pulse functions (BPFs), a new stochastic operational matrix is proposed. The nonlinear stochastic integral equation is converted into a nonlinear algebraic equation by this method. Furthermore, error analysis is given by the pathwise approach. Finally, two numerical examples exhibit the validity and accuracy of the approach.
2020 ◽
Vol 28
(3)
◽
pp. 209-216
2019 ◽
Vol 17
(03)
◽
pp. 1950007
◽
2012 ◽
Vol 12
(04)
◽
pp. 1250004
◽
2012 ◽
Vol 55
(3-4)
◽
pp. 791-800
◽
2016 ◽
Vol 24
(2)
◽
2020 ◽
Vol 90
◽
pp. 105346