Imprecise Markov Semigroups and their Ergodicity

arXiv:2405.00081v1 Announce Type: cross
Abstract: We introduce the concept of imprecise Markov semigroup. It allows us to see Markov chains and processes with imprecise transition probabilities as (a collection of diffusion) operators, and thus to unlock techniques from geometry, functional analysis, and (high dimensional) probability to study their ergodic behavior. We show that, if the initial distribution of an imprecise Markov semigroup is known and invariant, under some conditions that also involve the geometry of the state space, eventually the …

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