WIAS Preprint No. 2768, (2020)

Quantitative heat kernel estimates for diffusions with distributional drift

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Authors

• Perkowski, Nicolas
• van Zuijlen, Willem
  ORCID: 0000-0002-2079-0359

2010 Mathematics Subject Classification

• 60H10 35A08

Keywords

• Heat kernel bound, singular diffusion, parametrix method

DOI

10.20347/WIAS.PREPRINT.2768

Abstract

We consider the stochastic differential equation on ℝ ^d given by d X _t = b(t,X_t ) d t + d B_t, 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 Γ_t and prove upper and lower heat kernel bounds for Γ_t with explicit dependence on t and the norm of b.

Appeared in

• Potential Anal., published online on 27.01.2022 (2022), DOI 10.1007/s11118-021-09984-3 .

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