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- W4301701187 abstract "In this paper we consider the It^o SDE $$d X_t=d W_t+b(t,X_t),d t, quad X_0=xin {mathbb R}^d,$$ where $W_t$ is a $d$-dimensional standard Wiener process and the drift coefficient $b:[0,T]times{mathbb R}^dto{mathbb R}^d$ belongs to $L^q(0,T;L^p({mathbb R}^d))$ with $pgeq 2, q>2$ and $frac dp +frac 2q<1$. In 2005, Krylov and Rockner cite{KR05} proved that the above equation has a unique strong solution $X_t$. Recently it was shown by Fedrizzi and Flandoli cite{FF13b} that the solution $X_t$ is indeed a stochastic flow of homeomorphisms on ${mathbb R}^d$. We prove in the present work that the Lebesgue measure is quasi-invariant under the flow $X_t$." @default.
- W4301701187 created "2022-10-05" @default.
- W4301701187 creator A5006671485 @default.
- W4301701187 date "2014-01-08" @default.
- W4301701187 modified "2023-10-14" @default.
- W4301701187 title "Quasi-invariance of the stochastic flow associated to It^o's SDE with singular time-dependent drift" @default.
- W4301701187 doi "https://doi.org/10.48550/arxiv.1401.1884" @default.
- W4301701187 hasPublicationYear "2014" @default.
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