On time inhomogeneous stochastic Itô equations with drift in L_d+1

2020/05/18 by Н. В. Крылов, Krylov, N. V. · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #60H10 #60J60 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2005.08831

openalex publication_date 2020/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 the solvability belongs to A.V. Skorokhod. Weak uniqueness of solutions is an open problem even if the diffusion is constant.

Citations

• On stochastic equations with drift in L_d

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• Maximum principle for non-uniformly parabolic equations and applications

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