Buckdahn, Rainer Anticipative Girsanov transformations. (English) Zbl 0722.60059 Probab. Theory Relat. Fields 89, No. 2, 211-238 (1991). 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 \(d_ c(-DK)\). Reviewer: R.Buckdahn (Berlin) Cited in 3 ReviewsCited in 13 Documents MSC: 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:transformation of the Gaussian measure; anticipative stochastic calculus; Skorokhod integral PDF BibTeX XML Cite \textit{R. Buckdahn}, Probab. Theory Relat. Fields 89, No. 2, 211--238 (1991; Zbl 0722.60059) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.