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- W4287998166 abstract "We consider singular SDEs like begin{equation} label{ss} dX_t = b(t, X_t) dt + A X_t dt + sigma(t) d{L}_t , ;; t in [0,T], ;; X_0 =x in {mathbb R}^n, end{equation} where $A$ is a real $n times n $ matrix, i.e., $A in {{mathbb R}}^n otimes {{mathbb R}}^n$, $b$ is bounded and Holder continuous, $sigma : [0,infty) to {{mathbb R}}^n otimes {{mathbb R}}^d $ is a locally bounded function and $L= ({L}_t)$ is an ${mathbb R}^d$-valued L'evy process, $1 le d le n$. We show that strong existence and uniqueness together with $L^p$-Lipschitz dependence on the initial condition $x $ imply Davie's uniqueness or path by path uniqueness. This extends a result of [E. Priola, AIHP, 2018] proved when $n=d$, $A=0$ and $sigma(t) equiv I $. We apply the result to some singular degenerate SDEs associated to the kinetic transport operator $ frac{1}{2} triangle_v f + $ ${v cdot partial_{x}f} $ $+F(x,v)cdot partial_{v}f $ when $n =2d $ and $L$ is an ${{mathbb R}}^d$-valued Wiener process. For such equations strong existence and uniqueness are known under Holder type conditions on $b$. We show that in addition also Davie's uniqueness holds." @default.
- W4287998166 created "2022-07-26" @default.
- W4287998166 creator A5009752389 @default.
- W4287998166 date "2019-12-05" @default.
- W4287998166 modified "2023-09-24" @default.
- W4287998166 title "On Davie's uniqueness for some degenerate SDEs" @default.
- W4287998166 doi "https://doi.org/10.48550/arxiv.1912.02776" @default.
- W4287998166 hasPublicationYear "2019" @default.
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