Some properties of solutions of It\^o equations with drift in $L_{d+1}$

N. V. Krylov

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arXiv · 2011.04589

Some properties of solutions of It\^o equations with drift in $L_{d+1}$

N. V. Krylov

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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 $L_{d+1}(\mathbb{R}^{d+1})$. Here we study some properties of these processes such as higher summability of Green's functions, boundedness of resolvent operators in Lebesgue spaces, establish It\^o's formula, and so on.

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BibTeX RIS

N. V. Krylov. 2020-11-09. Some properties of solutions of It\^o equations with drift in $L_{d+1}$. https://arxiv.org/abs/2011.04589

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