On Time Inhomogeneous Stochastic Itô Equations with Drift in LD+1

N. V. Krylov

doi:10.1007/s11253-021-01864-8

On Time Inhomogeneous Stochastic Itô Equations with Drift in L_D+1

N. V. Krylov

Mathematics

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4 Scopus citations

Abstract

We prove the solvability of Itô stochastic equations with uniformly nondegenerate bounded measurable diffusion and drift in L_d+1(R^d+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.

Original language	English (US)
Pages (from-to)	1420-1444
Number of pages	25
Journal	Ukrainian Mathematical Journal
Volume	72
Issue number	9
DOIs	https://doi.org/10.1007/s11253-021-01864-8
State	Published - Feb 2021

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Publisher Copyright:
© 2021, Springer Science+Business Media, LLC, part of Springer Nature.

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