Quantitative Heat-Kernel Estimates for Diffusions with Distributional Drift
Tóm tắt
We consider the stochastic differential equation on
$\mathbb {R}^{d}$
given by
$$ \begin{array}{@{}rcl@{}} \mathrm{d} X_{t} = b(t,X_{t}) \mathrm{d} t + \mathrm{d} B_{t}, \end{array} $$
where B is a Brownian motion and b is considered to be a distribution of regularity
$ > -\frac 12$
. We show that the martingale solution of the SDE has a transition kernel Γt and prove upper and lower heat-kernel estimates for Γt with explicit dependence on t and the norm of b.
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