From Collatz-Weilandt to Donkser-Varadhan via Krein-Rutman

摘要

The `value' of infinite horizon risk-sensitive control is the principal eigenvalue of a certain positive operator. This facilitates the use of Chang's extension of the Collatz-Weilandt formula to derive a variational characterization thereof. For the uncontrolled case, this reduces to the Donsker-Varadhan functional.