We prove the solvability of Itô stochastic equations with uniformly nondegenerate bounded measurable diffusion and drift in Ld+1(Rd+1). Actually, the powers of summability of the drift in x and t could be different. Our results seem to be new even if the diffusion is constant. The method of proving solvability belongs to A.V. Skorokhod. Weak uniqueness of solutions is an open problem even if the diffusion is constant.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 9, pp. 1232–1253, September, 2020. Ukrainian DOI: 10.37863/umzh.v72i9.6280.
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Krylov, N.V. On Time Inhomogeneous Stochastic Itô Equations with Drift in LD+1. Ukr Math J 72, 1420–1444 (2021). https://doi.org/10.1007/s11253-021-01864-8
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DOI: https://doi.org/10.1007/s11253-021-01864-8