The characterization of equilibrium potentials and last exit distributions for elliptic diffusion processes (Q1767766)

Let \(X\) be an elliptic diffusion on \({\mathbb R}^d, d \geq 3,\) and let \(L\) be its last exit time from the unit ball around the starting point. The authors are interested in precise estimates on the function \(t^{d2} {\mathbb P}[L> t]\) when \(t\to +\infty\), and in particular on the existence of moments for \(L\). The tools use an extremal representation of \(U\mu_K\) where \(U\) is the potential kernel of \(X\) and \(\mu_K\) the equilibrium measure of a compact set \(K\) with respect to \(X\).