Almost Supermartingale Extensions of Olivier's Theorem

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. --- Source: arXiv:2607.02489v1 - http://arxiv.org/abs/2607.02489v1 PDF: https://arxiv.org/pdf/2607.02489v1 Original Link: http://arxiv.org/abs/2607.02489v1