Abstract
We consider finite element approximations for a one-dimensional second-order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index H ≤ 1/2. We make use of a sequence of approximate solutions with the fractional noise replaced by its piecewise constant approximations to construct the finite element approximations for the equation. The error estimate of the approximations is derived through rigorous convergence analysis.
| Original language | English |
|---|---|
| Pages (from-to) | 184-197 |
| Number of pages | 14 |
| Journal | IMA Journal of Numerical Analysis |
| Volume | 38 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 25 Jan 2018 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© The authors 2017. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Keywords
- Finite element approximation
- Fractional Brownian motion
- Piecewise constant approximation
- Stochastic differential equation of boundary value type
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