Some notes on Lamperti's recurrence of stochastic sequences

The present study provides another look on Lamperti’s theorem on recurrence or transience of stochastic sequences. We establish connection between Lamperti’s theorem and the recent result by the author [V. M. Abramov, A new criterion for recurrence of Markov chains with infinitely countable set of states. \emph{Theor. Probab. Math. Stat.} \textbf{112} (2025), 1–15].

💡 Research Summary

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The paper revisits Lamperti’s classic 1960 recurrence–transience criterion for non‑negative discrete‑time stochastic processes and connects it with a much more recent recurrence test introduced by the same author (Abramov, 2025) for countable‑state Markov chains. Lamperti’s theorem states that, under the existence of a second moment, the process is recurrent if the conditional first moment μ(x) satisfies
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