2020/02/13 by Natan T’Joens, T'Joens, Natan, Jasper De Bock +1
Biochemistry, Genetics and Molecular Biology · Computer Science · #Bayesian Modeling and Causal Inference #FOS: Mathematics #Formal Methods in Verification #Gene Regulatory Network Analysis #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2002.05661
openalex publication_date 2020/02/13 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
We study the limit behaviour of upper and lower bounds on expected time\naverages in imprecise Markov chains; a generalised type of Markov chain where\nthe local dynamics, traditionally characterised by transition probabilities,\nare now represented by sets of 'plausible' transition probabilities. Our main\nresult is a set of necessary and sufficient conditions under which these upper\nand lower bounds, called upper and lower expected time averages, will converge\nas time progresses towards infinity to limit values that do not depend on the\nprocess' initial state. Remarkably, our conditions are considerably weaker than\nthose needed to establish similar results for so-called limit -- or steady\nstate -- upper and lower expectations, which are often used to provide\napproximate information about the limit behaviour of time averages as well. We\nshow that such an approximation is sub-optimal and that it can be significantly\nimproved by directly using upper and lower expected time averages.\n