what is $\mathcal{F}_t^0$-optional positive process $\tilde a(q)$ defined in Hayashi et al?

Question

In the paper ofHayashi et al. in assumption D is defined the following convergence in probability $A(q)_t^n \overset{\mathbb{P}}\to \int_{0}^{t} a(q)_s ds$. what does it means the process $a(q)$ is $\mathcal{F}_t^0$-optional positive process?