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On potentials of Itô’s Processes with Drift in Ld+ 1

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Abstract

This paper is a natural continuation of Krylov (2020), where strong Markov processes are constructed in the time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in \(L_{d+1}(\mathbb {R}^{d+1})\). Here we study some properties of these processes such as the probability to pass through narrow tubes, higher summability of Green’s functions, and so on. The results seem to be new even if the diffusion is constant.

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Acknowledgements

The author is sincerely grateful to the referees for their comments which helped improve the presentation.

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  1. University of Minnesota, 127 Vincent Hall, Minneapolis, MN, 55455, USA

    N. V. Krylov

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  1. N. V. Krylov
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Correspondence to N. V. Krylov.

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Krylov, N.V. On potentials of Itô’s Processes with Drift in Ld+ 1. Potential Anal 59, 283–309 (2023). https://doi.org/10.1007/s11118-021-09968-3

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  • DOI: https://doi.org/10.1007/s11118-021-09968-3

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