Quantitative heat kernel estimates for diffusions with distributional drift

2020/09/22 by Perkowski, Nicolas, van Zuijlen, Willem · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2009.10786

Abstract

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

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