  We consider a multivariate distributional recursion of sum-type as arising in
the probabilistic analysis of algorithms and random trees. We prove an upper
tail bound for the solution using Chernoff's bounding technique by estimating
the Laplace transform. The problem is traced back to the corresponding problem
for binary search trees by stochastic domination. The result obtained is
applied to the internal path length and Wiener index of random b-ary recursive
trees with weighted edges and random linear recursive trees. Finally, lower
tail bounds for the Wiener index of these trees are given.
