Abstract
If $(u_n)^\infty_{n=0}$ is a null-recurrent renewal sequence, we prove that there exist two null-recurrent renewal sequences $(\nu_n)^\infty_{n=0}$ and $(w_n)^\infty_{n=0}$ such that $(u_n\nu_n)^\infty_{n=0}$ is null-recurrent and $(u_n w_n)^\infty_{n=0}$ is transient.
Citation
Gerard Letac. "Recurrence for Products of Renewal Sequences." Ann. Probab. 5 (4) 591 - 594, August, 1977. https://doi.org/10.1214/aop/1176995768
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