A Strong Law for the Size of Yule M-Oriented Recursive Trees

Let N_t be the total number of nodes in a Yule m-oriented recursive tree at time t. Then {N_t : t ∈ [0;1)} is a Yule process with birth rates λ_n = (m(n - 1) + 1)λ for n ≥ 1, where N₀ = 1. In this paper, we first give the exact distribution of N_t, then prove that , almost surely