A probabilistic ergodic decomposition result

Computability of the ergodic decomposition

The study of ergodic theorems from the viewpoint of computable analysis is a rich field of investigation. Interactions between algorithmic randomness, computability theory and ergodic theory have recently been examined by several authors. It has been observed that ergodic measures have better computability properties than non-ergodic ones. In a previous paper we studied the extent to which non-...

Randomness and the Ergodic Decomposition

We briefly present ongoing work about Martin-Löf randomness and the ergodic decomposition theorem. In [ML66], Martin-Löf defined the notion of an algorithmically random infinite binary sequence. The idea was to have an individual notion of a random object, an object that is acceptable as an outcome of a probabilistic process (typically, the tossing of a coin). This notion has proved successful,...

A Guide to the Ergodic Decomposition Theorem: Ergodic Measures as Extreme Points

On Probabilistic Completeness of Probabilistic Cell Decomposition

Probabilistic Cell Decomposition (PCD) is a probabilistic path planning method combining the concepts of approximate cell decomposition with probabilistic sampling. It has been shown that the use of lazy evaluation techniques and supervised sampling in important areas result in a high performance path planning method. Even if it was postulated before that PCD is probabilistically complete, we p...

A Decomposition Theorem for Probabilistic Transition Systems

In this paper we prove that every nite Markov chain can be de composed into a cascade product of a Bernoulli process and several simple permutation reset deterministic automata The original chain is a state homomorphic image of the product By doing so we give a positive answer to an open question stated in Paz concerning the decomposability of probabilistic systems Our result is based on the ob...