We revisit a simply stated problem of Knuth. Previous approaches rely on the Bernoulli nature of the underlying stochastic process to recover the systems mean behaviour. We show that limiting results hold for a wide range of stochastic processes. A Large Deviation Principle (LDP) is proved, allowing estimates to be made for the probability of rare-events. From the LDP, a weak law of large numbers is deduced.
|Number of pages||12|
|Journal||Mathematical Proceedings of the Royal Irish Academy|
|Publication status||Published - Nov 2004|
- Banach's matchbox problem
- large deviation principles