What question did this study set out to answer?

The aim is to explore conditions under which unique ergodicity occurs in noninvertible stochastic dynamical systems.

Unique ergodicity for random noninvertible maps on an interval

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The aim is to explore conditions under which unique ergodicity occurs in noninvertible stochastic dynamical systems.
Investigated noninvertible stochastic systems on the unit interval
Provided conditions for unique ergodicity based on mean injectivity
Presented specific examples demonstrating failure of unique ergodicity
Established a condition for unique ergodicity in certain injective systems
Identified cases where unique ergodicity does not hold

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This note investigates unique ergodicity in noninvertible stochastic systems, suggesting conditions for its occurrence.

Brofferio et al. (2026) studied this question.

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