Geodesic
Non-commutative Ito and Stratonovich noise and stochastic evolutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 2, pp. 276-284

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We complete the theory of non-commutative stochastic calculus by introducing the Stratonovich representation. The key idea is to develope a theory of white noise analysis, for both the Ito and Stratonovich representations, which is based on distributions over piecewise continuous functions mapping into a Hilbert space. As an example, we give a derive the most general class of unitary stochastic evolutions, when the Hilbert space is the space of complex numbers, by first constructing the evolution in the Stratonovich representation where unitarity is self-evident. 
@article{TMF_1997_113_2_a3,
     author = {J. Gough},
     title = {Non-commutative {Ito} and {Stratonovich} noise and stochastic evolutions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {276--284},
     publisher = {mathdoc},
     volume = {113},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_113_2_a3/}
}
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J. Gough. Non-commutative Ito and Stratonovich noise and stochastic evolutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 2, pp. 276-284. http://geodesic.mathdoc.fr/item/TMF_1997_113_2_a3/