Derives heat-kernel bounds and Schauder estimates for SDEs with L^∞ C^β drifts in the Young regime via non-Levi parametrix, implying weak well-posedness, irreducibility and strong Feller property.
Quantitative heat kernel estimates for diffusions with distributional drift
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
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 $\Gamma_t$ and prove upper and lower heat kernel bounds for $\Gamma_t$ with explicit dependence on $t$ and the norm of $b$.
verdicts
UNVERDICTED 2representative citing papers
The total mass U(t) of the 2D parabolic Anderson model with white-noise potential satisfies log U(t) ~ χ t log t almost surely as t → ∞, with χ from a variational formula also governing the principal eigenvalue on expanding boxes.
citing papers explorer
-
On Heat kernel Estimtes for Brownian SDEs with Distributional Drift
Derives heat-kernel bounds and Schauder estimates for SDEs with L^∞ C^β drifts in the Young regime via non-Levi parametrix, implying weak well-posedness, irreducibility and strong Feller property.
-
Longtime asymptotics of the two-dimensional parabolic Anderson model with white-noise potential
The total mass U(t) of the 2D parabolic Anderson model with white-noise potential satisfies log U(t) ~ χ t log t almost surely as t → ∞, with χ from a variational formula also governing the principal eigenvalue on expanding boxes.