Many complex systems display fluctuations between alternative states in correspondence to tipping points. These critical shifts are usually associated with generic empirical phenomena such as strengthening correlations between entities composing the system. In finance, for instance, market...

The statistical properties of a stochastic process may be described (1) by the expectation values of the observables, (2) by the probability distribution functions or (3) by probability measures on path space. Here an analysis of level (3) is carried out for market fluctuation processes. Gibbs...