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

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  • Krylov, N.V.

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.

Suggested Citation

  • Krylov, N.V., 2022. "Some properties of solutions of Itô equations with drift in Ld+1," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 363-387.
    • Handle: RePEc:eee:spapps:v:147:y:2022:i:c:p:363-387
    DOI: 10.1016/j.spa.2022.01.021
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    1. Krylov, N.V., 2021. "On stochastic Itô processes with drift in Ld," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 1-25.
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