Consider the SDE:
\begin{equation}
dv_t = k(\theta - v_t) dt + \xi \sqrt{v_t} dW^{v}_{t}
\end{equation}
It describes a process $v_t$ which is a strictly positive if the drift is stronger enough, i.e. if drift parameters ($k$, the speed of mean-reverting, and $\theta$, mean-reverting level) and the Vol-of-Vol $\xi$ satisfy:
\begin{equation}
k \theta > \frac{1}{2} \xi^2
\end{equation}
which is known as *Feller condition*.
I know this condition can be generalized to multi-factor affine processes.
For example, if the volatility of the returns $\log S_t$ is made of several independent factors $v_{1,t},v_{2,t},...,v_{n,t}$, then the Feller condition applies to each factor separately (check here at page 705, for example).
Moreover Duffie and Kan (1996) provide a multidimensional extension of the Feller condition.

But I still don't understand if we still need the (or a sort of) Feller condition in case of **jump-diffusion**. You may consider for example the simple case of a volatility factor with exponentially distributed jumps:
\begin{equation}
dv_t = k(\theta - v_t) dt + \xi \sqrt{v_t} dW^{v}_{t} + dJ^{v}_{t}
\end{equation}
where $J^{v}_{t}$ is a compound Poisson process, independent of the Wiener $W^{v}_{t}$. The Poisson arrival intensity is a constant $\lambda$ with mean $\gamma$.
I observe that in this case, the long term mean reverting level is jump-adjusted:
\begin{equation}
\theta \Longrightarrow \theta ^{*}=\theta + \frac{\lambda}{k} \gamma
\end{equation}
so I suspect if a sort of Feller condition applies it must depends on jumps.

Nevertheless, from a purely intuitive perspective, even if the barrier at $v_t = 0$ is absorbent, jump would pull back from 0 again.

Thanks for your time and attention.

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