On limit theorems under the Shilkret integral

The Shilkret integral or idempotent expectation is a sublinear functional which is very close to being a sublinear expectation since it satisfies all the required properties but its domain is not a linear space. In this paper, we prove that it admits a law of large numbers which is structurally similar to Peng’s LLN for sublinear expectations although significant differences exist. As regards the central limit theorem, the situation is radically different as the $ \sqrt n$ normalization can lead to a trivial limit and other normalizations are possible for variables with a finite second moment or even bounded.