  Let $u = \{u(t, x); (t,x)\in \mathbb R_+\times \mathbb R\}$ be the solution
to a linear stochastic heat equation driven by a Gaussian noise, which is a
Brownian motion in time and a fractional Brownian motion in space with Hurst
parameter $H\in(0, 1)$. For any given $x\in \mathbb R$ (resp. $t\in \mathbb
R_+$), we show a decomposition of the stochastic process $t\mapsto u(t,x)$
(resp. $x\mapsto u(t,x)$) as the sum of a fractional Brownian motion with Hurst
parameter $H/2$ (resp. $H$) and a stochastic process with
$C^{\infty}$-continuous trajectories. Some applications of those decompositions
are discussed.
