Rates of Convergence for Chains of Expansive Markov Operators

Abstract

We provide conditions that guarantee local rates of convergence in distribution of iterated random functions that are not nonexpansive mappings in locally compact Hadamard spaces. Our results are applied to stochastic instances of common algorithms in optimization, stochastic tomography for X-FEL imaging, and a stochastic algorithm for the computation of Fréchet means in model spaces for phylogenetic trees.

arXiv comment29 pages, 75 references. Accepted to Transactions of Mathematics and its Applications. This is a more narrowly focused version of arXiv:2007.06479. arXiv admin note: text overlap with arXiv:2205.15897