t

\(\begin{aligned} & \lambda_v(n, t) = \mu_v+\sum_{v^{\prime} \in \mathbf{V}} \sum_{n^{\prime} \in \mathbf{N}} \sum_{k=0}^K \alpha_{v^{\prime}, v, k} \hat{A}_{n^{\prime}, n}^k \int_{t^{\prime} \in \mathbf{T}_{t^{-}}} \kappa\left(t-t^{\prime}\right) d C_{v^{\prime}}\left(n^{\prime} t^{\prime}\right)\end{aligned}\)