Geodesic
The stochastic approach for non-hamiltonian systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 153-159

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The stochastic quantization of dissipative systems is discussed. It is shown that in order to stochastically quantize a system with dissipation, one has to restrict the Fourier transform of the space-time variable to the positive half domain in the complex plane. This breaks the time-reversal invariance, which manifests in the formulation through the resulting noninvariant forms for the propagators. The relation of the stochastic approach with the Caldeira and Leggett path-integral method is also analyzed. 
@article{TMF_1994_100_1_a14,
     author = {R. Tzani},
     title = {The stochastic approach for non-hamiltonian systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {153--159},
     publisher = {mathdoc},
     volume = {100},
     number = {1},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a14/}
}
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R. Tzani. The stochastic approach for non-hamiltonian systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 100 (1994) no. 1, pp. 153-159. http://geodesic.mathdoc.fr/item/TMF_1994_100_1_a14/