WIAS Preprint No. 2768, (2020)

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.

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