Strong laws of large numbers for sub-linear expectations

Abstract

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.

10 pages

References in corpus (1)

• A strong law of large numbers for capacities

Cited by in corpus (7)

• The convergence of the sums of independent random variables under the sub-linear expectations
• Convergence for sums of i. i. d. random variables under sublinear expectations
• An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation
• Ergodicity of Invariant Capacity
• Ergodicity of Sublinear Markovian Semigroups
• Some inequalities and limit theorems under sublinear expectations
• Strong law of large numbers for $m$-dependent and stationary random variables under sub-linear expectations