Geodesic
Conditionally positive-definite functions in quantum probability theory
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", Tome 36 (1989), pp. 103-147 Cet article a éte moissonné depuis la source Math-Net.Ru

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The author introduces the concepts of positive-definite and conditionally positive definite functions with values in the algebra of bounded maps of a $C^*$-algebra. An analog of Schoenberg's theorem is proved, a GNS-representation is obtained for conditionally positive-definite functions in terms of suitable cocycles, and this representation leads to a noncommutative generalization of the Lévy–Khinchin formula. Applications to the problem of continuous measurement in quantum mechanics are considered. A complete mathematical description is presented of continuous measurement processes, based on the analogy with the classical parts of probability theory — the theory of infinitely divisible distributions and functional limit theorems for processes with independent increments. 
@article{INTD_1989_36_a3,
     author = {A. S. Holevo},
     title = {Conditionally positive-definite functions in quantum probability theory},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {103--147},
     year = {1989},
     volume = {36},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1989_36_a3/}
}
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A. S. Holevo. Conditionally positive-definite functions in quantum probability theory. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", Tome 36 (1989), pp. 103-147. http://geodesic.mathdoc.fr/item/INTD_1989_36_a3/