On stochastic It\^o processes with drift in $L_{d}$

N. V. Krylov

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arXiv · 2001.03660

On stochastic It\^o processes with drift in $L_{d}$

N. V. Krylov

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Abstract

For It\^o stochastic processes in $\mathbb{R}^{d}$ with drift in $L_{d}$ Aleksandrov's type estimates are established in the elliptic and parabolic settings. They are applied to estimating the resolvent operators of the corresponding elliptic and parabolic operators in $L_{p}$ and $L_{p+1}$, respectively, where $p\geq d$.

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N. V. Krylov. 2020-01-10. On stochastic It\^o processes with drift in $L_{d}$. https://arxiv.org/abs/2001.03660

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