Geodesic
Quantization of stationary Gaussian random processes and their generalizations
Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 479-516

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We consider quantization of stationary Gaussian random processes whose physical counterparts are states of open systems in equilibrium with the environment. For this, we propose a formalism and its physical interpretation in accordance with the concept of Hamiltonian modeling. The method is universal and includes the known models as particular cases. We also consider extending the method applicability domain to linear systems with infrared singularities of two-point functions. In particular, fractal Brownian motions constitute a family of reference models in this class.
Keywords: open system, Hamiltonian modeling, Gaussian flow, quasifree state of the algebra of canonical commutation relations, fractal Brownian motion. 
@article{TMF_2012_173_3_a8,
     author = {A. I. Oksak},
     title = {Quantization of stationary {Gaussian} random processes and their generalizations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {479--516},
     publisher = {mathdoc},
     volume = {173},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a8/}
}
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A. I. Oksak. Quantization of stationary Gaussian random processes and their generalizations. Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 479-516. http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a8/