Sharp inequality for randomly stopped sums of independent non-negative random variables

AbstractIn this paper we shall prove a moment inequality which in a special case yields the following result E∑k=1τξkp≤2p−1E∑k=1τ'ξkp, 1 ≤ p < ∞, where (ξk) is a sequence of independent non-negative random variables, τ is a stopping time, and τ' is a copy of τ independent of the sequence (ξk). The constant 2p−1 is best possible