Rates of Convergence for Chains of Expansive Markov Operators

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.