Some properties of solutions of Itô equations with drift in L_d+1

2020/11/09 by N. V. Krylov, Krylov, N. V.
Economics, Econometrics and Finance · Mathematics · #60H10 #60J60 #Advanced Harmonic Analysis Research #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2011.04589

openalex publication_date 2020/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a natural continuation of [8], where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in L_d+1(ℝ^d+1). Here we study some properties of these processes such as higher summability of Green's functions, boundedness of resolvent operators in Lebesgue spaces, establish Itô's formula, and so on.

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