Maximum Entropy Principles for Markov Processes

Abstract

We shall discuss in some simple cases what may be called the limit law of “typical paths” which contribute to an expression of the form

$$ E(\exp(TF({Y_T})))$$

for large T≧0. Here the Y_T, T ≧ 0, are random elements with values in a suitable space and satisfy a large deviation principle, vaguely speaking of the form

$$P({Y_T} \sim x){\text{ }} \sim {\text{ }}\exp ({\text{ - }}Th(x))$$

h being the so-called entropy function. F is a function with values in [−∞,∞).