Supports of super Ornstein-Uhlenbeck processes (Q1902258)

Some results on the supports of super Ornstein-Uhlenbeck processes \((X_t)_{t \geq 0}\) are obtained. First we obtain the probability of \(X_\bullet\) ever charges [\(\overline {B}(0,R)]^c\), then we consider a positive radical solution of the singular elliptic boundary value problem which plays a key role in the estimation of the probability, and we give a convergence estimation of the solution near \(x = R\); we also prove that \(\bigcup_{t \geq 0} (\text{supp }X_t)\) is bounded \(P_\mu\)-a.s.