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 is an element of [0; infinity) } is a Yule process with birth rates lambda(n) = (m (n-1) + 1) lambda for n >= 1, where N-0 = 1. In this paper, we first give the exact distribution of N-t, then prove thatlim (t infinity) ln N-t/ m lambda t = 1; almost surely