Geodesic
Generalized solutions of Gibbs type for the Bogolyubov–Strel'tsova diffusion hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 3, pp. 398-420 
V. I. Skripnik. Generalized solutions of Gibbs type for the Bogolyubov–Strel'tsova diffusion hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 58 (1984) no. 3, pp. 398-420. http://geodesic.mathdoc.fr/item/TMF_1984_58_3_a8/
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     title = {Generalized solutions of {Gibbs} type for the {Bogolyubov{\textendash}Strel'tsova} diffusion hierarchy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A generalized solution is constructed for the hierarchy of coupled diffusion equations for the sequence of correlation functions of interacting particles diffusing in a fluid. At the initial time, this solution is identical to Gibbs correlation functions. The solution is obtained in the form of a series in powers of the activity, and the series converges uniformly over a finite time interval.

[1] Streltsova E. A., UMZh, XI:1 (1959), 83–92

[2] Chandrasekar S., Stokhasticheskie problemy v fizike i astronomii, IL, M., 1949, 168 pp.

[3] Ginibre J., J. Math. Phys., 6:2 (1965), 239–251 ; “Some application of functional integration in statistical mechanics”, Statistical Mechanics and Quantum Field Theory, eds. C. Dewitt, R. Stora, Gordon and Breach, Leshouches, 1970, 327–427

[4] Ryuel D., Statisticheskaya mekhanika. Strogie rezultaty, Mir, M., 1971, 367 pp.

[5] Gikhman I. I., Skorokhod A. V., Stokhasticheskie differentsialnye uravneniya, Naukova dumka, Kiev, 1968, 354 pp. | MR | Zbl