 for an arbitrary but fixed subsequence $\left\{ n_{k}\right\} _{k\in \mathbb{N}}\subset \mathbb{N}$, there is a sub-subsequence $\left\{ n_{k_{i}}\right\} _{i\in \mathbb{N}}\subset \mathbb{N}$ such that $$\begin{array}{ccc} D_{t-}^{\left( n_{k_{i}}\right) }\theta _{0}^{\left( n_{k_{i}}\right) }\left( t,x\right) & \overset{\lambda \times \nu \times \mathbb{P}\text{-a.s.}}{\longrightarrow } & D_{t-}\theta _{0}\left( t,x\right) , \\ D_{t-}^{\left( n_{k_{i}}\right) } & \overset{\lambda \times \mathbb{P}\text{-a.s.}}{\longrightarrow } & D_{t-}