Kingman's subadditive ergodic theorem
In mathematics, Kingman's subadditive ergodic theorem is one of several ergodic theorems. It can be seen as a generalization of Birkhoff's ergodic theorem. Intuitively, the subadditive ergodic theorem is a kind of random variable version of Fekete's lemma (hence the name ergodic). As a result, it can be rephrased in the language of probability, e.g. using a sequence of random variables and expected values. The theorem is named after John Kingman.
Statement of theorem
for -a.e. x, where g(x) is T-invariant. If T is ergodic, then g(x) is a constant.
If we take , then we have additivity and we get Birkhoff's pointwise ergodic theorem.
- S. Lalley, Kingman's subadditive ergodic theorem lecture notes, http://galton.uchicago.edu/~lalley/Courses/Graz/Kingman.pdf
- Pitman, Lecture 12: Subadditive ergodic theory, http://www.stat.berkeley.edu/~pitman/s205s03/lecture12.pdf