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

N. V. Krylov

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

Probability 2020-01-31 v2

Authors: N. V. Krylov

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 $p\geq d$ .

Keywords

markov processes stochastic processes

Cite

@article{arxiv.2001.03660,
  title  = {On stochastic It\^o processes with drift in $L_{d}$},
  author = {N. V. Krylov},
  journal= {arXiv preprint arXiv:2001.03660},
  year   = {2020}
}

Comments

27 pages, some misprints are corrected, references added

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