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This article is concerned with the \emph{asymptotically autonomousrobustness} (almost surely and in probability) of non-autonomous randomattractors for two stochastic versions of 3D convective Brinkman-Forchheimer(CBF) equations defined on the whole space $\mathbb{R}^3$:  $$\frac{\partial\boldsymbol{v}}{\partial t}-\mu\Delta\boldsymbol{v}+(\boldsymbol{v}\cdot\nabla)\boldsymbol{v}+\alpha\boldsymbol{v}+ \beta|\boldsymbol{v}|^{r-1}\boldsymbol{v}+\nablap=\boldsymbol{f}(t)+``\mbox{stochastic terms}",\quad\nabla\cdot\boldsymbol{v}=0,$$  with initial and boundary vanishing conditions, where $\mu,\alpha,\beta >0$,$r\geq1$ and $\boldsymbol{f}(\cdot)$ is a given time-dependent external forcefield. By the asymptotically autonomous robustness of a non-autonomous randomattractor $ \mathscr{A}=\{ \mathscr{A}(\tau,\omega): \tau\in\mathbb{R},\omega\in\Omega\}$ we mean its time-section $\mathscr{A}(\tau,\omega)$ isrobust to a time-independent random set as time $\tau$ tends to negativeinfinity according to the Hausdorff semi-distance of the underlying space. Ourgoal is to study this topic, almost surely and in probability, for thenon-autonomous 3D CBF equations when the stochastic term is a linearmultiplicative or additive noise, and the time-dependent forcing convergestowards a time-independent function. Our main results contain two cases: i)$r\in(3,\infty)$ with any $\beta,\mu>0$; ii) $r=3$ with $2\beta\mu\geq1$. Themain procedure to achieve our goal is how to justify that the usual pullbackasymptotic compactness of the solution operators is uniform on some\emph{uniformly} tempered universes over an \emph{infinite} time-interval$(-\infty,\tau]$. This can be done by a method based on Kuratowski's measure ofnoncompactness.

Asymptotically autonomous robustness in Probability of non-autonomous  random attractors for stochastic convective Brinkman-Forchheimer equations on  $\mathbb{R}^3$