On the Backward Interpolation Equations for the Jump Component of a Markov Process

A Markov processes $(\theta_t,\nabla_t)$ with $\theta_t$ being a jump Markov process and $\nabla_t$ defined by the Ito equation (1) is considered.
For the conditional probabilities $\pi_{\alpha}(t,\tau)$ and $\pi_{\alpha\beta}(t,\tau)$ the equation (3) and (4) are arived.
The existence and uniqueness of a solution of the system (5) is proved.