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Invariant sublinear expectations
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DOI：10.1016/j.spa.2026.104943.png)
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Abstract
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We first investigate the structure of a T-invariant sublinear expectation r = supP is an element of Theta EP on (Omega, H) by constructing its periodic components and studying their basic properties. We then show that every continuous strongly ergodic sublinear expectation (see Definition 4.5) admits a finite period pr, that is, r[f - f degrees Tpr] = 0, f is an element of H. Moreover, the corresponding set of representing probabilities Theta coincides with the convex hull of finitely many Tpr-ergodic probability measures. As an application of the characterization, we establish an ergodicity theorem stating that the limit of the pr-step time means achieves the upper expectation P-a.s. for some P is an element of Theta.
Keywords:
Invariant sublinear expectation
Periodic decomposition
Strong ergodicity
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