The maximum entropy method applied to stationary density computation

The maximum entropy method (maxent) is widely used in the context of the moment problem which appears naturally in many branches of physics and engineering; it is used to numerically recover the density with least bias from finitely many known moments. We introduce the basic idea behind this method and apply this method to approximating fixed densities of Markov operators in stochastic analysis and Frobenius–Perron operators in ergodic theory of chaotic dynamics.