For stochastic adaptive systems important is to consider local ergodic system, Markov chain, local Monte Carlo simulation and maximum entropy method to be more efective.
We can derive many set of actions that give ergodic subsystems, but the problem is in which case they are optimal under some criteria.
The less ergodic a process is, the more important Markov chain, local Monte Carlo simulation and maximum entropy methods become (and vice versa)
I was thinking on local ergodic process ( local controllability, local irreducibility). See my paper in Analele Universitati din Timisoara, 1990, Ser. Mat.Inf.
Local controllability, local ergodicity is necessary condition for the system, such that fixed point theorem holds true. The fixed point theorem is the equivalent of the maximum entropy principle. Am I right?
Under the conditions of local controllability, local ergodicity, follows for linearized case , the possibility of local stabilizability.
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