论文标题
分布漂移的扩散的定量热内核估计
Quantitative heat kernel estimates for diffusions with distributional drift
论文作者
论文摘要
我们考虑$ \ Mathbb {r}^d $上的随机微分方程。 - \ frac12 $。我们表明，SDE的Martingale解决方案具有过渡内核$γ_T$，并以$γ_T$的价格证明了上下热的内核边界，明确依赖于$ t $，而$ b $的标准则是$ t $。
We consider the stochastic differential equation on $\mathbb{R}^d$ given by $$ \, \mathrm{d}X_t = b(t,X_t) \, \mathrm{d}t + \, \mathrm{d} B_t, $$ where $B$ is a Brownian motion and $b$ is considered to be a distribution of regularity $ > -\frac12$. We show that the martingale solution of the SDE has a transition kernel $Γ_t$ and prove upper and lower heat kernel bounds for $Γ_t$ with explicit dependence on $t$ and the norm of $b$.
