What is meant by ergodic process?

A process in which every sequence or sizable sample is equally representative of the whole (as in regard to a statistical parameter).

What is an ergodic matrix?

Ergodic Markov Chains. Defn: A Markov chain is called an ergodic or irreducible Markov chain if it is possible to eventually get from every state to every other state with positive probability. Ex: The wandering mathematician in previous example is an ergodic Markov chain.

How do you write ergodic literature?

Ergodic literature is defined as requiring non-trivial effort to navigate. If a traditional novel requires trivial effort to navigate – simply reading the words in the order written – then an ergodic text is handled in ways that demand greater effort from the reader.

How do you show Markov chain is ergodic?

Defn: A Markov chain with finite state space is regular if some power of its transition matrix has only positive entries. P(going from x to y in n steps) > 0, so a regular chain is ergodic. To see that regular chains are a strict subclass of the ergodic chains, consider a walker going between two shops: 1 ⇆ 2.

What is unique about ergodic literature?

One of the major innovations of the concept of ergodic literature is that it is not medium-specific so long as the medium has the ability to produce an iteration of the text. New media researchers have tended to focus on the medium of the text, stressing that it is for instance paper-based or electronic.

What means ergodic literature?

What does ergodic mean in Markov chain?

A Markov chain is said to be ergodic if there exists a positive integer such that for all pairs of states in the Markov chain, if it is started at time 0 in state then for all , the probability of being in state at time is greater than .

Are ergodic Markov chains irreducible?

Ergodic Markov chains are also called irreducible. A Markov chain is called a regular chain if some power of the transition matrix has only positive elements.

What are the applications of ergodic theory in physics?

In geometry, methods of ergodic theory have been used to study the geodesic flow on Riemannian manifolds, starting with the results of Eberhard Hopf for Riemann surfaces of negative curvature. Markov chains form a common context for applications in probability theory.

What is ergodic linear operator topology?

The ergodic means, as linear operators on Lp ( X, Σ, μ) also have unit operator norm; and, as a simple consequence of the Birkhoff–Khinchin theorem, converge to the projector ET in the strong operator topology of Lp if 1 ≤ p ≤ ∞, and in the weak operator topology if p = ∞.

What are deterministic and ergodic dynamical systems?

The notion of deterministic dynamical systems assumes that the equations determining the dynamics do not contain any random perturbations, noise, etc. Thus, the statistics with which we are concerned are properties of the dynamics. Ergodic theory, like probability theory, is based on general notions of measure theory.

What are the consequences of the ergodic theorem?

Another consequence of the ergodic theorem is that the average recurrence time of A is inversely proportional to the measure of A, assuming that the initial point x is in A, so that k0 = 0. (See almost surely .) That is, the smaller A is, the longer it takes to return to it.