$$\begin{aligned} P_{\tilde{v}j}(\tilde{v})  &  =\partial P(\tilde{v})/\partial\tilde{v}_{j},\text{ }\pi_{0}=\Pr(y_{t0}=0),\text{ }\lambda_{00}(x)=E[y_{0t}|x_{t+0}=x],\\ \lambda_{j0}(x)  &  =E[A(x_{t})P_{\tilde{v}j}(\tilde{v}_{t})\frac{y_{tj}}{P_{j}(\tilde{v}_{t})}|x_{t+0}=x],(j=0,...,J).\