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Inverse diffusion and direct derivation of stochastic liouville equations

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Literature cited

  1. B. L. Rozovskii, “Liouville's equations for a Markov diffusion process,” in: Fourteenth All-Union Colloquium-School on Probability Theory and Mathematical Statistics, Bakuriani (1980), Abstracts of Reports, Metsniereba, Tbilisi (1980), pp. 26–28.

  2. B. L. Rozovskii, “On the first integrals and Liouville equations for diffusion processes,” Abstracts Third Working Conference on Stochastic Differential Systems, Visegrad, Hungary (1980), SZAMKI, Budapest (1980), pp. 77–80.

    Google Scholar 

  3. N. V. Krylov and B. L. Rozovskii, “On the first integrals and Liouville equations for diffusion processes,” Lecture Notes in Control and Information Sciences,36, 117–125, Springer-Verlag, Berlin (1981).

    Google Scholar 

  4. H. McKean, Stochastic Integrals [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  5. M. A. Krasnosel'skii and A. V. Pokrovskii, “On natural solutions of stochastic equations,” Dokl. Akad. Nauk SSSR,240, No. 2, 264–267 (1978).

    Google Scholar 

  6. M. A. Krasnosel'skii and A. V. Pokrovskii, “Vibration-stable differential equations with a continuous right-hand side,” Tr. Mosk. Mat. O-va,27, 93–112 (1972).

    Google Scholar 

  7. N. V. Krylov and B. L. Rozovskii, “On Cauchy's problem for linear stochastic partial differential equations,” Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 6, 1329–1347 (1977).

    Google Scholar 

  8. Yu. N. Blagoveshchenskii and M. I. Freidlin, “Some properties of parameter-dependent diffusion processes,” Dokl. Akad. Nauk SSSR,138, No. 3, 508–511 (1961).

    Google Scholar 

  9. I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations [in Russian], Naukova Dumka, Kiev (1968).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 33, No. 5, pp. 773–779, May, 1983.

The author expresses his gratitude to N. V. Krylov and B. L. Rozovskii for useful discussions.

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Veretennikov, A.Y. Inverse diffusion and direct derivation of stochastic liouville equations. Mathematical Notes of the Academy of Sciences of the USSR 33, 397–400 (1983). https://doi.org/10.1007/BF01158290

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