The maximum of a critical branching Wiener process
A critical branching Wiener process on \(\mathbb{R}\), starting from a single particle situated at 0, is studied (i.e., critical binary branching of all particles occurs at all discrete times \(n=1,2,\dots)\). Limit theorems are derived for the spatially rescaled empirical measures and for the maximal position at time \(n\) as \(n\to\infty\), conditioned on non-extinction. As mentioned, the limiting rescaled position of the right most particle by time \(n\) had been studied under more general conditions by \textit{H. Kesten} [ibid. 8, No. 4, 921-962 (1995; Zbl 0857.60087)].
scientific article; zbMATH DE number 1234276