Quantitative heat kernel estimates for diffusions with distributional drift
- Perkowski, Nicolas
- van Zuijlen, Willem
2010 Mathematics Subject Classification
- 60H10 35A08
- Heat kernel bound, singular diffusion, parametrix method
We consider the stochastic differential equation on ℝ d given by d X t = b(t,Xt ) d t + d Bt, where B is a Brownian motion and b is considered to be a distribution of regularity > - 1/2. We show that the martingale solution of the SDE has a transition kernel Γt and prove upper and lower heat kernel bounds for Γt with explicit dependence on t and the norm of b.
- Potential Anal., published online on 27.01.2022 (2022), DOI 10.1007/s11118-021-09984-3 .