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

N.V. Krylov

Stochastic Processes and their Applications, 2022, vol. 147, issue C, 363-387

Abstract: This paper is a natural continuation of Krylov (2020), where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in Ld+1(Rd+1). Here we study some properties of these processes such as higher summability of Green’s functions, a maximum principle for related transport equations with irregular coefficients, boundedness of resolvent operators in Lebesgue spaces, establish Itô’s formula, and so on.

Keywords: Itô’s equations with singular drift; Markov diffusion processes; Transport equation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.01.021

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