Super-Brownian local time: a representation and two applications (Q1781641)

There are three different notions \(L_t, \mathcal{L}_t, l_t\) of the local time of super-Brownian motion. A rigorous meaning of \(L_t\) was given by \textit{R. J. Adler} and \textit{M. Lewin} [Stochastic Processes Appl. 41, 45--67 (1992; Zbl 0754.60086)]. The notions \(\mathcal{L}_t\) and \(l_t\) were introduced by \textit{I. Iscoe} [Probab. Theory Relat. Fields 71, 85--116 (1986; Zbl 0555.60034)] and \textit{E. B. Dynkin} [in: Les processus stochastiques. Astérisque 157--158, 147--171 (1988; Zbl 0659.60105)], respectively. In the paper under review the authors use a semimartingale representation of local time to show that the three notions of local time are equivalent.