Local reconstruction theorem in the absence of mathematical expectation (Q1945208)

This paper concerns random walks \(\{S_n\}\) whose steps \(\{X_k\}\) are mixed geometric distributions with infinite expectation. Theorem 1 provides an expression for \(u_n=\sum_{k=0}^\infty P(S_k=n)\), under certain assumptions, and Theorem 2 provides asymptotics for the same in the case in which the summands are a mixture of a mixture of geometric distributions and a distribution, that is, concentrated on the lattice of nonnegative integers.