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Let $u = \{u(t, x); (t,x)\in \mathbb R_+\times \mathbb R\}$ be the solutionto a linear stochastic heat equation driven by a Gaussian noise, which is aBrownian motion in time and a fractional Brownian motion in space with Hurstparameter $H\in(0, 1)$. For any given $x\in \mathbb R$ (resp. $t\in \mathbbR_+$), 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 Hurstparameter $H/2$ (resp. $H$) and a stochastic process with$C^{\infty}$-continuous trajectories. Some applications of those decompositionsare discussed.

A note on decompositions of the stochastic convolution driven by a white-fractional Gaussian noise