Geodesic
Dilations of Contraction Cocycles and Cocycle Perturbations of the Translation Group of the Line
Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 3-18

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The class of contraction cocycles which can be dilated to unitary Markovian cocycles of a translation group $S$ on the straight line is introduced. The class of cocycle perturbations of $S$ by unitary Markovian cocycles $W$ with the property $W_t-I\in\mathscr S_2$ (the Hilbert–Schmidt class) is investigated. The results are applied to perturbations of Kolmogorov flows on hyperfinite factors generated by the algebra of canonical anticommutation relations. 
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     author = {G. G. Amosov and A. D. Baranov},
     title = {Dilations of {Contraction} {Cocycles} and {Cocycle} {Perturbations} of the {Translation} {Group} of the {Line}},
     journal = {Matemati\v{c}eskie zametki},
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G. G. Amosov; A. D. Baranov. Dilations of Contraction Cocycles and Cocycle Perturbations of the Translation Group of the Line. Matematičeskie zametki, Tome 79 (2006) no. 1, pp. 3-18. http://geodesic.mathdoc.fr/item/MZM_2006_79_1_a0/