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Anticipative Girsanov transformations. (English) Zbl 0722.60059
The transformation of the measure induced by $$(W+\int^{\bullet}_{0}K_ sds)$$ with $$(K_ s)$$ possibly anticipating the Wiener process $$(W_ s)$$ is discussed, a Girsanov type theorem under rather weak assumptions on $$(K_ s)$$ is derived and the density of this transformation is computed, which includes an explicit expression for the Carleman-Fredholm determinant $$d_ c(-DK)$$.

MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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References:
 [1] Buckdahn, R.: Transformations on the Wiener space and Skorohodtype stochastic differential equations. Seminarbericht 105, Sekt. Math., Humboldt-Universität Berlin, 1989 · Zbl 0685.60062 [2] Gihman, I.I., Skorohod, A.W.: Densities of probability measures in functional spaces. Usp. Mat. Nauk6, 83-156 (1966) [3] Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Amsterdam: North-Holland 1981 · Zbl 0495.60005 [4] Kusuoka, s.: The non-linear transformation of Gaussian measure on Banach space and its absolute continuity (1). J. Fac. Sci., Univ. Tokyo. Sect. IA.29, 567-597 (1982) · Zbl 0525.60050 [5] Meyer, P.A.: Probability and potentials. Waltham: Blaisdell 1966 · Zbl 0138.10401 [6] Nualart, D.: Noncausal stochastic integrals and calculus. In: Korezlioglu, H., Ustunel, A.S. (eds.) Stochastic analysis and related fields. Proceedings, Silivri 1986 (Lect. Notes Math., vol. 1316, pp. 80-129) Berlin Heidelberg New York: Springer 1988 [7] Nualart, D., Pardoux, E.: Stochastic calculus with anticipating integrands. Probab. Th. Rel. Fields79, 535-581 (1988) · Zbl 0629.60061 · doi:10.1007/BF00353876 [8] Nualart, D., Zakai, M.: Generalized stochastic integrals and the Maliiavin calculus. Robab. Th. Rel. Fields73, 255-280 (1986) · Zbl 0601.60053 · doi:10.1007/BF00339940 [9] Ramer, R.: On non-linear transformations of Gaussian measures. J. Funkt. Anal.15, 166-187 (1974) · Zbl 0288.28011 · doi:10.1016/0022-1236(74)90017-2
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