Infinitesimal generators of random positive semigroups (Q1378361)

The author extends results from \textit{Y. Kifer} and himself [in: Stochastic analysis and applications, 270-285 (1996)] to random positive semigroups with not necessarily independent increments. He shows that in this more general situation such semigroups have random infinitesimal operators which are semimartingales with values in integro-differential operators, namely, they can be represented as a sum of a second order stochastic partial differential operator and a random integral operator involving a Lévy measure and a counting measure. In the last section the author studies the intrinsic meaning of coefficients of random generators when only the differential part is present.