Summary
Let σ andb be bounded processes on the Wiener space (Ω,ℱP), Ω=C([0,1]), which are possibly anticipating the Brownian motionW t (ω)=ω(t), and let η be a bounded random variable. We deduce the existence and uniqueness of a solutionX for the linear equation with Skorohod integral
under rather weak assumptions on σ and no additional requirement onb and η. The description of the solutionX requires to study the family {T t ,t∈[0,1]} of transformationT t of Ω into itself associated to (1) by the equation
.
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Buckdahn, R. Linear skorohod stochastic differential equations. Probab. Th. Rel. Fields 90, 223–240 (1991). https://doi.org/10.1007/BF01192163
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DOI: https://doi.org/10.1007/BF01192163