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We consider finite element approximations for a one dimensional second orderstochastic differential equation of boundary value type driven by a fractionalBrownian motion with Hurst index $H\le 1/2$. We make use of a sequence ofapproximate solutions with the fractional noise replaced by its piecewise con-stant approximations to construct the finite element approximations for theequation. The error estimate of the approximations is derived through rigorousconvergence analysis.

Finite element approximations for second order stochastic differential equation driven by fractional Brownian motion