On the density of probability measures of diffusion-type processes
Izvestiya. Mathematics , Tome 3 (1969) no. 5, pp. 1055-1066.

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In this paper we obtain a formula (9) for the derivative $\varphi_t(\omega)$, with respect to Wiener measure, of the Radon–Nikodým measure corresponding to the diffusion type process (1).
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R. Sh. Liptser; A. N. Shiryaev. On the density of probability measures of diffusion-type processes. Izvestiya. Mathematics , Tome 3 (1969) no. 5, pp. 1055-1066. http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a6/

[1] Kolmogorov A. N., Osnovnye ponyatiya teorii veroyatnostei, ONTI, M., 1936

[2] Gikhman I. I., Skorokhod A. V., Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1965 | MR | Zbl

[3] Stratonovich R. L., Uslovnye markovskie protsessy i ikh primenenie k teorii optimalnogo upravleniya, MGU, M., 1966 | MR

[4] Liptser R. Sh., Shiryaev A. N., “Nelineinaya filtratsiya diffuzionnykh markovskikh protsessov”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 104, 1968, 135–180 | Zbl

[5] Shiryaev A. N., “Issledovaniya po statisticheskomu posledovatelnomu analizu”, Matemat. zametki, 3:6 (1968), 739–754 | Zbl

[6] Shiryaev A. N., “Stokhasticheskie uravneniya nelineinoi filtratsii skachkoobraznykh markovskikh protsessov”, Problemy peredachi informatsii, II:3 (1966), 3–22

[7] Kallianpur G., Striebel C., “Estimation of stochastic systems; arbitrary system processes with additive white noise observation errors”, AMS, 39:3 (1968), 786–801 | MR

[8] Kallianpur G., Striebel C., “Stochastic differential equations occuring in the estimation of continuous parameter stochastic processes”, Teor. Verojatnost. and Primenen., 14 (1969), 597–622 | MR | Zbl

[9] Skorokhod A. V., Issledovaniya po teorii sluchainykh protsessov, KGU, Kiev, 1961

[10] Cameron R. H., Graves R. E., “Additive functionals on a space of continuous functions. I”, TAMS, 70 (1951), 160–176 | DOI | MR | Zbl

[11] Loev M., Teoriya veroyatnostei, IL, M., 1962

[12] Dub Dzh. L., Veroyatnostnye protsessy, IL, M., 1956

[13] Dynkin E. B., Markovskie protsessy, Fizmatgiz, M., 1963 | MR

[14] Bellman R., Kuk K. L., Differentsialno-raznostnye uravneniya, Mir, M., 1967 | MR | Zbl