Summary
Given strong uniqueness for an Itô's stochastic equation with discontinuous coefficients, we prove that its solution can be constructed on “any” probability space by using, for example, Euler's polygonal approximations. Stochastic equations in ℝd and in domains in ℝd are considered.
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Research supported by the Hungarian National Foundation of Scientific Research No. 2990.
Supported in part by NSF Grant DMS-9302516
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Gyöngy, I., Krylov, N. Existence of strong solutions for Itô's stochastic equations via approximations. Probab. Th. Rel. Fields 105, 143–158 (1996). https://doi.org/10.1007/BF01203833
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DOI: https://doi.org/10.1007/BF01203833