Abstract
For the Itô stochastic equations in with drift in , several results are discussed, such as the existence of weak solutions, the existence of the corresponding Markov process, the Aleksandrov type estimates of their Green’s functions, which yield their summability to the power of , the Fabes–Stroock type estimates, which show that Green’s functions are summable to a higher degree, the Fanghua Lin type estimates, which are one of the main tools in the -theory of fully nonlinear elliptic equations, the fact that Green’s functions are in the class of Muckenhoupt and a few other results.
Acknowledgments
The author thanks T. Yastrzhembskiy for pointing out several mistakes and misprints in the first draft of the paper. My thanks are also due to Pill Gyu Jung, who kindly pointed out some inconsistencies in the original proof of Theorem 4.1 and to the two referees for exemplary work which allowed me to improve and correct the presentation.
Citation
N.V. Krylov. "On stochastic equations with drift in ." Ann. Probab. 49 (5) 2371 - 2398, September 2021. https://doi.org/10.1214/21-AOP1510
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