Abstract
Let σ ∈ C 4 b(R1). We provide assumptions on the random variable G and the process b = (b t (x)) possibly anticipating the driving Wiener process (W t ) under which the anticipative stochastic differential equation with Skorohod integral 21-1
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References
Buckdahn, R.: Transformations on the Wiener space and Skorohodtype stochastic differential equations. Seminarbericht 105, Sekt. Math., Humboldt-Univ. Berlin 1989
Buckdahn, R.: Anticipative Girsanov transformations. Probab. Theory Relat. Fields 89 (1991), 211–238
Buckdahn, R.: Skorohod Stochastic Differential Equations of Diffusion Type. To appear in Probab. Theory Relat. Fields
Buckdahn, R.: Anticipative Girsanov Transformation and Stochastic Differential Equations. Seminarbericht 92-2, Fachbereich Mathematik, Humboldt-Univ. Berlin 1992
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 (1982), 567–597
Nualart, D.; Pardoux, E.: Stochastic calculus with anticipating integrands. Probab. Theory Relat. Fields 78 (1988), 535–582
Nualart, D.; Pardoux, E.: Boundary value problems for stochastic differential equations. Ann. Probab. 19 (1991) 3, 1118–1144
Ocone, D.; Pardoux, E.: A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations. Ann. Inst. Henri Poincaré, Probab. Stat. 25 (1989), 39-71
Pardoux, E.: Applications of anticipating stochastic calculus to stochastic differential equations. Preprint 1989
Shiota, Y.: A linear stochastic differential equation containing the extended Itô integral. Math. Rep., Toyama Univ. 9 (1986), 43–65
Ustunel, A.S.: Some comments on the filtering of diffusions and the Malliavin calculus. In: Korezlioglu, H.; Ustunel, A.S. (eds.) Proc. Silivri Conf. 1986. — Berlin, Heidelberg, New York: Springer 1988, 247–266 (Lect. Notes Math., 1316)
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Buckdahn, R. (1993). Nonlinear Skorohod Stochastic Differential Equations. In: Nualart, D., Solé, M.S. (eds) Barcelona Seminar on Stochastic Analysis. Progress in Probability, vol 32. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8555-3_2
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DOI: https://doi.org/10.1007/978-3-0348-8555-3_2
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