How about Brownian excursions?http://en.m.wikipedia.org/wiki/Brownian_excursion Just as the number of left parentheses seen is always greater or equal the number of right ones, the excursion has always moved up more than down.
Formally too, the Catalan numbers can be used to count the discrete excursions as well as the bracketings. See for instance Shreve: Stochastic Calculus for Finance, volume I, chapter 5, and the discussion here: http://math.hawaii.edu/wordpress/bjoern/distribution-of-first-hitting-time/