TY - JOUR
AU - N. V. Krylov
PY - 2020/09/22
Y2 - 2022/09/27
TI - On time inhomogeneous stochastic Itô equations with drift in $L_{d+1}$
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 9
SE - Research articles
DO - 10.37863/umzh.v72i9.6280
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/6280
AB - UDC 519.21We prove the solvability of Itô stochastic equations with uniformly nondegenerate bounded measurable diffusion and drift in $L_{d+1}(R^{d+1}).$Actually, the powers of summability of the drift in $x$ and $t$ could be different. Our results seem to be new even if the diffusion is constant. The method of proving the solvability belongs to A. V. Skorokhod.Weak uniqueness of solutions is an open problem even if the diffusion is constant.
ER -