Numerical scheme for stochastic differential equations driven by fractional Brownian motion with \(1/4 < H < 1/2\). (English) Zbl 1464.60070
Summary: In this article, we study a numerical scheme for stochastic differential equations driven by fractional Brownian motion with Hurst parameter \(H \in (1/4, 1/2)\). Toward this end, we apply Doss-Sussmann representation of the solution and an approximation of this representation using a first-order Taylor expansion. The obtained rate of convergence is \(n^{-2H + \rho}\), for \(\rho\) small enough.
MSC:
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
Doss-Sussmann representation; fractional Brownian motion; stochastic differential equation; Taylor expansionReferences:
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