# ergodic

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Related to ergodic: Ergodic hypothesis

## er·god·ic

(ûr-gŏd′ĭk)
adj.
Of or relating to a system or process whose overall statistical properties can be determined by analysis of a sufficiently large sample of the states of one of its constituents or instances averaged over time.

[German Ergode, a set of points in a space with the property that all points will be included in a trajectory with equal frequency given a sufficient large number of trajectories (coined by Ludwig Eduard Boltzmann from Greek ergon, work; see werg- in Indo-European roots + Greek hodos, way, path) + -ic.]

er·god′i·cal·ly adv.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## ergodic

(ɜːˈɡɒdɪk)
adj
(Mathematics) maths of or relating to the probability that any state will recur
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## er•god•ic

(ɜrˈgɒd ɪk)

adj. Math., Statistics.
pertaining to the condition that, in an interval of sufficient duration, a system will return to states that are closely similar to previous ones: the basis of statistical methods used in modern dynamics and atomic theory.
[1925–30; erg- + Greek (h)od(ós) way, road + -ic]
er`go•dic′i•ty (-gəˈdɪs ɪ ti) n.
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Adj. 1 ergodic - positive recurrent aperiodic state of stochastic systems; tending in probability to a limiting form that is independent of the initial conditionsstatistics - a branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parametersrandom - lacking any definite plan or order or purpose; governed by or depending on chance; "a random choice"; "bombs fell at random"; "random movements"
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
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Further, we investigate how transition dynamics shifted the equilibrium levels of employment and unemployment over time and across space, by deriving the ergodic distributions related to the observed labour market transitions in each country over the period.
In this section, key statistical properties of the model, e.g., the spatial cross-correlation function (CCF), temporal autocorrelation function (ACF), Wigner-Ville spectrum, and ergodic capacity under non-isotropic scattering conditions considering the impact of velocity variations will be derived.
Bou-Rabee and Vanden-Eijnden propose a strategy for simulating stochastic differential equations, adopting an approach that is more tailored to the probabilistic structure of the solution in order to design stable and (weakly) accurate schemes for their simulation that are both provably ergodic when the underlying stochastic differential equation is, and faithful to the geometry of their domain of integration.
In this paper, the system performance (in the term the achievable throughput, the outage probability, ergodic capacity) of a two-way decode-and-forward two-way relaying network over Rician fading channel under the hardware impairment effect is proposed, analysed and demonstrated in details.
With the aim of classifying objective and subjective expressions, a discrete ergodic HMM was employed.
(iii) (X, f) has a unique ergodic measure [mu] and [[phi].sub.*] [mu] and is the standard Lebesgue measure on T.
In Section 2, we present some lemmas concerning the existence of a global positive solution and ergodic stationary distribution.
(P2) Under what conditions, will system (5) have a unique ergodic stationary distribution?
Nonlinear operator theory applies to diverse nonlinear problems in many areas such as differential equations, nonlinear ergodic theory, game theory, optimization problems, control theory, variational inequality problems, equilibrium problems, and split feasibility problems.
This action is known to be ergodic (see for example [FTP82] and [FTP83]), but since the measure is not preserved, no theorem on the convergence of means of the corresponding unitary operators had been proved.
Bruck, Jr, A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spaces, Israel J.

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