Search results
Results from the WOW.Com Content Network
The ergodic decomposition theorem states that every ergodic system can be split into two parts: the conservative part, and the dissipative part. Mixing is a stronger statement than ergodicity. Mixing asks for this ergodic property to hold between any two sets A , B {\displaystyle A,B} , and not just between some set A {\displaystyle A} and X ...
In physics, statistics, econometrics and signal processing, a stochastic process is said to be in an ergodic regime if an observable's ensemble average equals the time average. [1] In this regime, any collection of random samples from a process must represent the average statistical properties of the entire regime.
Ergodic theory is often concerned with ergodic transformations.The intuition behind such transformations, which act on a given set, is that they do a thorough job "stirring" the elements of that set. E.g. if the set is a quantity of hot oatmeal in a bowl, and if a spoonful of syrup is dropped into the bowl, then iterations of the inverse of an ergodic transformation of the oatmeal will not ...
In physics and thermodynamics, the ergodic hypothesis [1] says that, over long periods of time, the time spent by a system in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e., that all accessible microstates are equiprobable over a long period of time.
In probability theory, a stationary ergodic process is a stochastic process which exhibits both stationarity and ergodicity.In essence this implies that the random process will not change its statistical properties with time and that its statistical properties (such as the theoretical mean and variance of the process) can be deduced from a single, sufficiently long sample (realization) of the ...
In signal processing, the coherence is a statistic that can be used to examine the relation between two signals or data sets. It is commonly used to estimate the power transfer between input and output of a linear system. If the signals are ergodic, and the system function is linear, it can be used to estimate the causality between the input ...
Usually winds would have to be 60 to 80 mph for the company to consider the de-energization of transmission lines, Powell said, adding that the readings Edison saw were lower than that. The Eaton ...
Bernoulli shifts are classified by their metric entropy. [ 11 ] [ 12 ] [ 13 ] See Ornstein theory for more. Krieger finite generator theorem [ 14 ] (Krieger 1970) — Given a dynamical system on a Lebesgue space of measure 1, where T {\textstyle T} is invertible, measure preserving, and ergodic.