{"ID":5676756,"CreatedAt":"2026-07-03T03:29:23.032456456Z","UpdatedAt":"2026-07-07T01:06:03.009715918Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.02489","arxiv_id":"2607.02489","title":"Almost Supermartingale Extensions of Olivier's Theorem","abstract":"Olivier's 1827 theorem provides a rate of convergence to zero of the general term of a decreasing summable sequence of positive reals. We derive stochastic extensions of this result in the context of almost supermartingales. The results are applied to the analysis of stochastic iterative processes.","short_abstract":"Olivier's 1827 theorem provides a rate of convergence to zero of the general term of a decreasing summable sequence of positive reals. We derive stochastic extensions of this result in the context of almost supermartingales. The results are applied to the analysis of stochastic iterative processes.","url_abs":"https://arxiv.org/abs/2607.02489","url_pdf":"https://arxiv.org/pdf/2607.02489v1","authors":"[\"Patrick L. Combettes\",\"Javier I. Madariaga\"]","published":"2026-07-02T17:53:09Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\"]","methods":"[]","has_code":false}