Geodesic
Excessive maps, ``arrival times'' and perturbation of dynamical semigroups
Izvestiya. Mathematics , Tome 59 (1995) no. 6, pp. 1311-1325.

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The notion of excessive map for dynamical semigroup is introduced, and it is shown that an excessive map defines an operation-valued measure describing the measurement of an “arrival time” related to the irreversible dynamics described by the semigroup. Any such arrival time determines a positive perturbation of the dynamical semigroup describing the dynamics after “arrivals”. Generators of the relevant perturbations are characterized, and several examples, both commutative and a non-commutative, are discussed, elucidating the problem of standard representation. 
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A. S. Holevo. Excessive maps, ``arrival times'' and perturbation of dynamical semigroups. Izvestiya. Mathematics , Tome 59 (1995) no. 6, pp. 1311-1325. http://geodesic.mathdoc.fr/item/IM2_1995_59_6_a9/

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