Geodesic
On the Backward Interpolation Equations for the Jump Component of a Markov Process
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 2, pp. 427-431

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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. 
@article{TVP_1973_18_2_a29,
     author = {V. A. Lebedev},
     title = {On the {Backward} {Interpolation} {Equations} for the {Jump} {Component} of a {Markov} {Process}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {427--431},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_2_a29/}
}
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V. A. Lebedev. On the Backward Interpolation Equations for the Jump Component of a Markov Process. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 2, pp. 427-431. http://geodesic.mathdoc.fr/item/TVP_1973_18_2_a29/